The Levelling Up Secretary gave the update as he unveiled a new Government scheme during his appearance on Sophy Ridge on Sunday.
The latest figures were up from 1,300 visas on Thursday.
Mr Gove spoke about the new Homes for Refugees scheme offering £350 a month to Britons who will give a room to a Ukrainian refugee escaping the war.
The Secretary of State for Levelling Up said it is expected the Government’s new sponsorship route will bring tens of thousands of Ukrainian refugees to the UK.
Asked for his estimate of the number of people who could come to the UK through the scheme, he told Sky’s Sophy Ridge on Sunday: “Tens of thousands.”
Children will receive education in UK schools and refugees will be entitled to full NHS health care, he said.
There would also be £10,000 per individual refugee given to local authorities, Mr Gove added.
He said: “There’ll be money available for local authorities… There will be just over £10,000 per individual available to local authorities.”
The politician said there were many “generous hearted” people in the UK who want to help.
He added: “I’m exploring what I can do. There will be lots of people are seeing what they can do. One in ten say they want to do something to help. It’s a significant commitment. We need to help people.”
Elsewhere in the interview, Mr Gove said Vladimir Putin is prepared to escalate to grisly options at his disposal and he is capable of terrible violence.
The Levelling Up Secretary said the Russian President is capable of “devastation on a terrible, terrible scale” as war entered its 18th day.
He added: “Vladimir Putin is prepared to escalate the grisly options at his disposal. It is vital to give our support to President Zelensky.
“We know from what Putin has done elsewhere. Devastation on a terrible, terrible scale. We need to demonstrate solidarity with Ukraine.
“We know Putin is capable of terrible violence. But again, I am not a military expert. I don’t want your viewers to think I would be the right person to get into a discussion about chemical welfare.”