The incident took place last night when the accused travelling in a car without number plate tried to overtake the cavalcade of the minister between Aurai and Mirzamurad regions, they said.
According to the police, the men tried to overtake the minister's car despite a warning by her security personnel.
The trio made indecent comments at Patel and misbehaved with the security men, they said.
Patel complained about the matter to Varanasi SSP
R K Bhardwaj, who launched a drive to trace the whereabouts of the trio.
The three were arrested by the Mirzamurad police and their car was confiscated, the police said.
The accused are being questioned, they added.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)