CCTV of the heist outside Debenhams in East Street on Monday 11 January has been released as detectives appeal for witnesses.
The driver of a security van was approached at about 14:15 GMT by a man who stole the cashbox.
Police are trying to trace anyone who saw a silver van, which was later abandoned in Russell Street.
No weapons were used in the raid and no one was injured.
Thieves escaped with £20,000 in a robbery in Southampton, police have revealed.