The blast occurred in a cultural centre repurposed for Russia's armed forces to store ammunition, state news agencies reported, citing local emergency services for the toll.
Another eight service personnel were still reported missing as of Sunday evening, the Interfax news agency reported.
"As a result of the unintentional detonation of a hand grenade by a sergeant in a dormitory ... a fire broke out. Sixteen servicemen, including the culprit, have been taken to hospital. Three more died," local emergency services said in a statement cited by news agencies.
The TASS news agency said local officials said "careless handling" of the grenade caused it to explode.
The 112 and Baza Telegram channels, linked to Russia's law enforcement agencies, said the dead and injured were conscripts called up to fight in Ukraine under a mobilization drive.
Reports did not say when the incident took place.
The Belgorod region borders the northeast of Ukraine, where the city of Kharkiv has been targeted by multiple Russian missile attacks since the invasion of Ukraine last February.
In October a gunman opened fire at one of the several military bases in the Belgorod region, killing 11 soldiers.
Fuel and ammunition stores there have also been rocked by explosions in what Moscow said were Ukrainian attacks. Kyiv, without claiming responsibility, has described them as "karma" for Russia's invasion.
