"All the entry and exit points to the court have been sealed and police is trying to check the whole premises for any more such things," a senior police official told IANS.
The grenades have been sent to be defused, an official of the Anti-Terrorism Squad (ATS) said.
A passer-by spotted the unclaimed bag under a chair near gate number one of the court and called the police.
While the police is saying that a probe is on, local intelligence unit (LIU) officials link the finding of the hand grenades to a possible gang war; they say Brijesh Singh and other mafia dons frequent the court for appearances in cases.
The possibility of a terror angle is being explored
The possibility of a terror angle is also being explored, an official said.
There was a bomb explosion in this court in 2007 in which some people were killed. All the cases listed for the day have been postponed to Monday.
Senior Superintendent of Police (SSP) Aakash Kulhari said a probe is underway and that security has been scaled up.
Varanasi is the parliamentary constituency of Prime Minister Narendra Modi.