Mortgage holidays started in March, allowing people to defer payments without affecting their credit rating. That respite from payments would end for the first applicants in June and the Treasury said the extension would provide certainty for those affected.
However, it said borrowers should still pay their mortgages if they were able.
The deferred payments will still have to be paid back later on, so mortgage customers will face higher bills once the so-called holiday comes to an end.
However, the Treasury was concerned an abrupt end to the scheme could produce a cliff-edge effect, with families facing money problems as bad, if not worse, as they did when the virus struck.
Christopher Woolard, interim chief executive at financial regulator the Financial Conduct Authority (FCA), said that if customers could afford to restart mortgage payments "it is in their best interests to do so".
"But where they can't, a range of further support will be available," he added.
The date for homeowners to apply to extend their mortgage holidays has also been extended, with customers able to apply until the end of July.
More than 1.8 million mortgage customers have taken advantage of the relief from making payments so far.
The banking body, UK Finance, estimates this is an average of £755 a month.