The Driver and Vehicle Agency (DVA) said inspections of lift faults in test centres did not provide "sufficient assurance" on the effectiveness of ongoing repairs.
An inspection of all vehicle lifts in NI's MoT centres previously detected "signs of cracking" in 48 of 55 lifts.
MoT exemption certificates are being issued so motorists are able to drive.
The DVA said anyone scheduled for a car or light vehicle MoT on Tuesday "should not attend".
Test on heavy goods vehicles and buses will continue.
Paul Duffy, chief executive of the DVA told BBC News NI: "This is hugely embarrassing for the DVA.
"I think we have a fairly good reputation and this is something that has tarnished that reputation.
Mr Duffy said he had sought assurances from the contractor responsible for supplying, maintaining and servicing the lifts that they were safe to use.
He said: "We were given that assurance when the initial repairs were taking place, but that assurance then was not forthcoming from the contractor this evening on further inspections of lifts today.
"On that basis we had no option but to suspend the tests."
He said Infrastructure Minister Nichola Mallon had asked for a second opinion "on the quality of the inspections that have taken place" and that the DVA was exploring all options, including how quickly new lifts could be purchased.
In a statement, Mr Duffy added: "The DVA recognises the considerable inconvenience and disruption this will cause for many people and sincerely apologises that it has been unable to rectify this situation more quickly.
"Given the urgency of this situation, we are asking the public to follow media, social media channels and nidirect for updates.
"Staff will also be kept fully informed by their centre managers."