The move had been expected and comes after the small Baltic state met the required financial criteria.
Latvia suffered a deep recession in the wake of the financial crisis that saw it receive an international bailout.
PM Valdis Dombrovskis imposed big public spending cuts that helped the recovery. Latvia is now one of the fastest-growing economies in the EU.
The European Commission and the European Central Bank are likely to decide on the request in June.
Latvia says it has met the five requirements needed to gain entry into the eurozone, which relate to levels of debt, deficit, inflation, long-term interest rates and having a stable peg to the euro.
Latvia's currency, the lat, has been pegged to the euro since 2005 and Mr Dombrovskis argues that joining is the next natural step.
However, opinion polls in the country suggest that nearly two-thirds of the population are against joining the single currency.
Latvia has formally applied to join the euro in 2014, in a move which could see it become the 18th member of the bloc.