Mark Carney said that the world was changing, and whether you were a "sceptic or an evangelist" on global warning, governments and investors should be aware of the possible effects on financial stability.
In the insurance industry, extreme weather events were becoming more costly, he said, with losses increasing from $10bn a year in the 1980s to $50bn in the last decade.
In banking, billions of pounds of loans to energy companies and mining businesses might have to be re-assessed.
Mr Carney said that wasn't a job for him, but for investors, who would need to be given more information.
The Governor said that the vast majority of oil and gas reserves already discovered could now be "stranded" if new rules on carbon emissions are enforced by governments.
The oil and gas would be unusable.
"There are near term risks that are so called tail risks, a series of extreme weather events, pandemics, others," Mr Carney told me.
"We have seen manifestations of those in the past.
"The point is the risks build with time, and they build more rapidly with inaction so climate change is a function of cumulative emissions, so the slower the action is today, the bigger the action has to be in the future.
"That would mean more abrupt change, that would mean bigger shocks to the value of financial assets, bigger strains on banks and insurance companies that are exposed to those assets, so what we're trying to do is to promote as smooth an adjustment as possible.
"And we think it can be done, and we think it can be done by providing better information."
Mr Carney's interview came as he gave a major speech to Lloyd's of London insurers.
In the speech he said that "climate change will threaten financial resilience and longer term prosperity".
"While there is time to act, the window of opportunity is finite and shrinking," he said.
Mr Carney is also the head of the Financial Stability Board, the global organisation of central bankers.
As said he will be raising the issue at the next meeting of the G20 group of the world's largest economies in November.
In December, government leaders will be meeting in Paris to discuss the next moves on controlling global warming.
Mr Carney told me that "he wouldn't be sitting here" in 20 or 30 years when the risks of global warming would be more apparent.
He even suggested that there could be legal challenges in the future - similar to asbestos claims now - over inaction on climate change and the impact on health or the value of businesses.
"This is the challenge," he said.
"Sitting here today, is it [global warming] the biggest risk? No it isn't.
"Is it one of the biggest risks in the future? Yes.
"The challenge is that if there's not action today or in the near future that risk in the medium term goes up and up and requires sharper action, more abrupt action, and a bigger hit to the economy and financial stability."
I asked Mr Carney whether global warming came under the remit of the Governor of the Bank of England.
He said it did - the stability of the insurance sector which is facing increasing costs and banks facing possible asset write-downs meant this was a matter of global financial stability. Bank of England governor - global economy at risk from climate change
The Governor of the Bank of England has entered the controversial world of climate change - telling the BBC that, if there is no action now, global warming could become one of the biggest risks to economic stability in the future.