The MV Pentalina had 60 people on board when it grounded at St Margaret's Hope on Saturday night.
Smoke had been detected in the engine room of the Pentland Ferries vessel beforehand.
The RMT maritime union has called for a thorough investigation into how the incident happened.
Emergency services, including lifeboats which took passengers ashore, were called to the scene at about 19:30 after the ferry issued a mayday message. It has since been refloated and berthed at St Margaret's Hope.
The Maritime and Coastguard Agency (MCA) said it would be assessing the extent of any damage and added: "While the facts haven't been established yet, initial reports from the operator point to the cause of the grounding being a sudden mechanical failure."
It defended the fact that the ferry had been issued with a passenger ship safety certificate following surveys of the vessel on 18 April.
"At this time the vessel met the standards required for issue of this certificate," it said.
It added that MCA surveyors would carry out initial fact-finding to establish the cause and circumstances surrounding the incident.
Gary Brown and his pregnant partner Lauren Haston were on board the Pentalina at the time of the accident.
The pair were out on the deck when they noticed smoke coming from the engine room followed by "flustered" members of the crew.
Mr Brown said it was some time before any information was given to those on board. One crew member then started "abruptly" telling passengers to "find something to hold onto".
He said he was "panicking inside", but tried to remain calm for his partner. He said "overall people were calm", but a "lack of communication" was worrying.
Within about an hour, the passengers were escorted off the ferry onto lifeboats and have now been told they can collect their cars and belongings from the vessel.
Pentland Ferries sails across the Pentland Firth from Gills Bay in Caithness to St Margaret's Hope on the Orkney Islands.
The Pentalina came back into service on Wednesday after time in dry dock to allow another ferry, the MV Alfred, to service other routes to islands on the west coast.
It suffered technical problems on Friday then on Saturday night the ferry grounded on the shoreline, about 100 yards (91m) from its destination in Orkney.
The 56 adults, three children, and a baby, as well as several dogs, were taken ashore by RNLI lifeboats.
There were no reports of injuries and passengers described the rescue operation as calm and professional.
A spokesman for the RMT said: "A thorough investigation will be needed to establish how this major incident aboard the Pentland Ferries vessel occurred."
Gordon Martin, Scottish Organiser for the RMT told BBC Scotland the union had "raised a number of safety concerns" over the years about the Pentalina.
He said: "A major disaster has been averted we could've had a real, real situation on our hands.
"We're going from a crisis to a farce in the ferry sector in Scotland at the moment," he added.
Last week, Pentland Ferries main vessel, the newer and larger catamaran MV Alfred, began a nine-month charter with CalMac on the west coast, which is costing the Scottish government £9m.
It is not clear when the MV Pentalina will return to service.
The MCA said the MV Pentalina was refloated at about 05:30 after being towed by a tug and taken to its berth in St Margaret's Hope.
A spokeswoman said there were no signs of pollution and added that the ferry would be surveyed to establish the extent of any damage.
She added that the Marine Accident Investigation Branch (MAIB) had been informed.
Coastguard teams from St Margaret's Hope, Stromness and Kirkwall and the Stromness and Longhope RNLI lifeboats were involved in the rescue.
Pentand Ferries said: "The vessel was moved from the beach to the linkspan at 6.30 this morning and is now undergoing a survey, from which we will know what (if any) damage has been sustained. Only when we know the extent of the problem, can we formulate a plan to resume service.
"The Maritime Coastguard Agency (MCA) is conducting a survey and the Marine Accident Investigation Branch are expected to arrive on Tuesday (2 May).
"We understand the impact this will have on the local community and those with travel plans. Our customer service team is currently contacting all pre-booked passengers to inform them of the situation. In the meantime, we thank everyone for their patience and understanding."
Transport Scotland said Pentland Ferries would assess the condition of the vessel and any next steps to determine whether there would be any loss of services on the Pentland Firth.
It said that any further action to support capacity to Orkney would be considered in due course.
A spokesperson said: "Ministers were quickly made aware of the incident involving the MV Pentalina and kept informed of developments throughout the night.
"We were relieved that all passengers and crew are safe and that arrangements were made to support passengers with onward travel. "We would also like to express our appreciation to all those involved in the evacuation, including RNLI crews and other emergency services."
Hayley Green, vice chairperson of Orkney's Local Emergency Co-ordination Group (OLECG) said: "The situation, including the impact on ferry provision across the Pentland Firth, will be reviewed over the coming days."
She praised the efforts of all agencies involved, including the local community and volunteer lifeboat crews.
Scottish Conservative MSP Jamie Halcro Johnston, who is from Orkney, said the incident exposed the "pitiful lack of resilience in Scotland's ferry network".
He said: "The Pentalina was only summoned back into action this week because the MV Alfred had to be seconded from Pentland Ferries to help plug gaps in the ageing, unreliable CalMac fleet.
"While it will be important to know just how this incident came about, my immediate concern is for what this means for Orkney and how long this vital link for our islands will be severed."
He added: "There are a number of questions the Scottish government needs to answer, including whether the £9m agreement between CalMac and Pentland Ferries allows for the MV Alfred to be recalled to Orkney early, or if the Alfred will stay on the west coast and Orkney will be left without a key service."
Orkney MSP Liam McArthur said there were also important questions for the Maritime and Coastguard Agency to answer over the fact that it had recently inspected and certified the Pentalina as fit for service.
He added: "Answers are required too from the Scottish government whose failure to procure new ferries in a timely fashion has left services both in the north and on the west coast extremely vulnerable. As a result islanders and island communities are left paying the price."
The MV Alfred ran aground in the Pentland Firth in Swona in July last year, with 97 people on board who were transferred to lifeboats.