Mr Sharma - who is leading COP26, the climate summit hosted by the UK this year - said the effects were already clear with floods, fires and heatwaves.
"We can't afford to wait two years, five years, 10 years - this is the moment," he told the Observer.
But he did not condemn the government for allowing more fossil fuel projects.
And he defended his decision to travel to more than 30 countries in seven months.
Mr Sharma's interview with the Observer comes ahead of a major report being released on Monday from the United Nations' climate change researchers.
The report is set to be the strongest statement yet from the UN group on the science of climate change - and will likely give details about how the world's oceans, ice caps and land will change in the next decades.
The summary has been approved in a process involving scientists and representatives of 195 governments, which - having signed off on the findings - will be under pressure to take more action at COP26 in November.
Doug Parr, chief scientist with Greenpeace UK, said "world leaders have done a terrible job of listening" to warnings about climate change.
"This year, this has to change. We don't need more pledges, commitments and targets - we need real action right here right now."
Wildfires are currently raging in Greece, forcing thousands to evacuate their homes - and fires have also been burning in Turkey and California in the US. This summer, western Europe also saw its worst flooding in decades, which killed dozens of people.
Mr Sharma said if urgent action was not taken, the consequences would be "catastrophic".
"I don't think there's any other word for it," he said. "You're seeing on a daily basis what is happening across the world. Last year was the hottest on record, the last decade the hottest decade on record."
He added: "We're seeing the impacts across the world - in the UK or the terrible flooding we've seen across Europe and China, or forest fires, the record temperatures that we've seen in North America. Every day you will see a new high being recorded in one way or another across the world."
Mr Sharma said the report released on Monday is "going to be the starkest warning yet that human behaviour is alarmingly accelerating global warming".
"I don't think we're out of time but I think we're getting dangerously close to when we might be out of time. We will see [from the IPCC] a very, very clear warning that unless we act now, we will unfortunately be out of time."
"Africa has been waiting for the rest of the world to catch up and act on climate change for years," Fredrick Njehu, Christian Aid's senior climate change and energy adviser for Africa, highlighting the "changing rainfall patterns or overbearing heat" endured by the continent in recent years.
He added: "The important thing now is that rich world governments make up for lost time and act quickly to reduce emissions and deliver promised financial support for the vulnerable."
Glasgow is set to host the COP26 summit in November - which is the UN climate change conference.
The summit is seen as vital if climate change is to be brought under control, and leaders from 196 countries will meet to try and agree action.
But campaigners have accused the UK of hypocrisy, as there are plans to tap a new oil field off Shetland. The government has also said more oil and gas wells can be drilled in the North Sea, and there are plans for a new coal mine in Cumbria.
Earlier this year, the global energy watchdog the International Energy Agency said there cannot be any new investment in oil, gas or coal projects if we want to limit global warming to 1.5C. Experts say the impacts of climate change are far more severe when the increase is greater than 1.5C.
Mr Sharma refused to criticise the government's plan for the projects, saying: "Future [fossil fuel] licences are going to have to adhere to the fact we have committed to go to net zero by 2050 in legislation.
"There will be a climate check on any licences."
Mr Sharma's interview comes after he was criticised for flying abroad for meetings - and visiting more than 30 countries in seven months.
However, since then some environmental campaigners including Greenpeace have defended him, saying face-to-face meetings are important to persuade other nations to tackle climate change.
Mr Sharma told the Observer that in-person meetings were "incredibly vital and actually impactful".
"It makes a vital difference, to build those personal relationships which are going to be incredibly important as we look to build consensus," he said.
It also emerged in the Sunday Mirror that Foreign Secretary Dominic Raab did not self-isolate after returning from France, which was on the amber plus list meaning all arrivals must quarantine.
A government spokesman said it was Mr Raab's job to represent the UK abroad and he followed Covid guidelines on return.
There is an exemption for ministers to avoid quarantine when returning from abroad.