Russia has introduced fines on transactions by Russian nationals who send money to overseas bank accounts.
Amendments to existing laws on financial controls stipulate fines ranging from 75% to 100% of any transfer to a foreign account which did not go through a Russian bank account.
This may affect those who rent flats in foreign cities or receive payments for freelance work from non-Russian firms.
The government is trying to stop capital flight and to fight corruption.
According to central bank estimates, capital flight in 2012 came to $56.8bn (£36.5bn).
But the government says the 2012 figure is an improvement on the previous year's figure of $80.5bn and on the 2008 figure of $133.7bn.
Overseas bank accounts for Russian bureaucrats are becoming increasingly popular, says BBC Russian's Ekaterina Drobinina in Moscow.
In his regular address to parliament in December 2012, Russian President Vladimir Putin promised to tighten controls on foreign savings by Russian officials.
On Tuesday, Mr Putin introduced a bill which forbids officials and their spouses from keeping money in foreign bank accounts. Those who get caught will be sacked, under the new rules.
However, the rule is easy to get round, experts say.
The law only makes it compulsory for Russian citizens to notify the tax authorities whenever an account in a foreign bank is opened.
But in the absence of disclosure, tax officials will have no idea about the existence of the account.
"If the person is not transferring money from Russia to the foreign account, and if he is not notifying the tax authorities, the government will never find out about this account," says Sergei Budylin, a senior lawyer at Roche & Duffay.
The only exception is in the case of a criminal investigation where law enforcement officials contact a foreign bank.
Since 2009, Russian government officials and their spouses have been required to report their income. And in 2012, Mr Putin signed a law making it compulsory for them to report their spending as well.