From now on, people in the US state will be able to apply for marriage licences remotely and clerks allowed to conduct ceremonies virtually.
Mr Cuomo joked that the decision meant there was now "no excuse" for couples not to tie the knot.
"You can do it by Zoom. Yes or no?" he said in his briefing on Saturday.
The decision comes after New York state extended lockdown measures until 15 May. More than 13,000 people have died of coronavirus in New York city alone.
Social media reaction to the decision was mixed.
Some questioned why couples would choose to hold weddings when their families and friends are unable to join them, or criticised the governor for not prioritising other decisions.
But others pointed out that during a pandemic, marriage could offer practical benefits, such as allowing couples to share health insurance coverage.