Police fear there could be several hundred thousand unregistered arms remaining from the 1990s Balkans wars.
"The interior ministry of Serbia appeals to all citizens who have hand grenades and other explosive devices not to dispose of them in garbage containers and other places," the interior ministry said in a statement on its website.
"Instead, they should only call the nearest police station and officers will come as soon as possible to safely take them away," the statement said, adding that they would not face charges.
A recently enacted law on gun possession offers amnesty to those handing over illegal weapons before June 4.
The law sets out a five-year jail term for illegal possession of arms and makes it harder to obtain a license to carry a gun.
More than a million licenses for weapons possession have been issued in the country of 7.2 million people.
