The main post office in North Road and nearby offices have been evacuated after reports of a man with a gun.
The road was closed while police made the area safe and searched a car.
Channel 4’s Krishnan Guru-Murthy tweeted: “In Brighton to interview @CarolineLucas and police cordon just gone up at the post office next door.”
A police spokeswoman said: “Police were called around 10.45am on Friday (May 26) concerned for a man in North Road in Brighton.
“The man attended Brighton Royal Mail delivery office with what was believed could be a gun. Officers located his car, also parked in North Road, and closed the road as precaution while they searched it.
“One man has been arrested on suspicion of possession of a firearm.
“The road has now reopened and members of the public are thanked for their patience.”