The firm said it "remains committed" to Google users in the country and told the BBC it has relocated engineers in other countries on previous occasions.
Google declined to say how many staff would be affected by the move.
In July this year, the Russian parliament passed a law requiring internet companies to store citizens' personal data inside the country.
The Kremlin has said the law is designed to aid data protection but critics have seen it as an attempt to censor internet access as the law would give the government powers to block sites which refused to comply.
Many tech companies store user data in huge data storage facilities around the world and do not link the location of the data to the location of the user, meaning that most users' data will not be kept in the same country as them.
Google will retain some staff including sales, marketing and support teams in its Russia office, according to the Wall Street Journal.
""We are deeply committed to our Russian users and customers and we have a dedicated team in Russia working to support them," said the firm in a statement.