Sources told the BBC that the company was trying to find replacement roles abroad for staff employed in Moscow.
Infosys has been under pressure to cease its Russian operations following the invasion of Ukraine.
And Mr Sunak has faced questions over wife Akshata Murty’s shares in the firm, which was founded by her father.
Earlier, Labour leader Sir Keir Starmer told Sky News it was important for the chancellor to reveal whether his family had been “benefiting from money made in Russia when the [UK] government has put in place sanctions” on firms and individuals following the invasion of Ukraine.
Mr Sunak told the BBC’s Newscast podcast this week that he had found criticism of his wife “very upsetting”, adding that he understood how film star Will Smith had felt when his own wife had been mocked by comedian Chris Rock at the Oscars over her medical condition.
Infosys, one of India’s biggest companies with a presence in about 50 countries, set up an engineering centre in Moscow in 2016 and it is thought that up to 100 people are employed there.
After Russia invaded Ukraine, many global IT firms suspended operations in the country, but Infosys has kept what it called “a small team… based out of Russia that services some of our global clients” until now.
“We do not have any active business relationships with local Russian enterprises,” it added in a recent statement.
A spokesperson for Infosys declined to comment on the decision to close the Moscow office or what its future involvement with companies operating in Russia would be.
Ms Murty’s shareholding of 0.9% of Infosys is estimated to be worth more than £400m.
A spokesperson for Mr Sunak has previously said neither she nor any members of her family “have any involvement in the operational decisions of the company.
But Labour and the Liberal Democrats have insisted the chancellor has questions to answer about whether his family benefits from the shareholding at a time when he is calling for UK businesses to divest from Russia.
Labour leader Sir Keir Starmer told Sky News it was “in the public interest” to do so.
He added: “I’m not attacking their family but I do want to know if the chancellor’s household is benefiting from money from a company that’s investing in Russia when the government is saying quite rightly that nobody should be doing that.”
The chancellor told Newscast that, being in public life, he was himself “fair game” for criticism, but it was “very upsetting and, I think, wrong for people to try and come at my wife”.
Infosys, which has offices in London, Edinburgh and Nottinghamshire, announced last year that it was hiring 1,000 extra staff in the UK.
India’s government, unlike the UK’s, has not condemned Russia’s invasion of Ukraine and did not vote against it at the United Nations Security Council.