The Scots-born politician was posing for pictures with people in Notting Hill, West London, when a man shouted a comment about the Holocaust and started to attack him, the spokesman said.
Police were quickly on the scene and made an arrest.
Mr Galloway last night made a statement at Notting Hill Police Station.
His spokesman said: "George was posing for pictures with people and this guy just attacked him, leapt on him and started punching him.
"It appears to be connected with his comments about Israel because the guy was shouting about the Holocaust."
He said he had no idea whether the attacker was an Israeli, an English Defence League supporter or had some other motivation for attacking the Bradford West MP.
Mr Galloway attracted attention earlier this month when he was interviewed by West Yorkshire Police following a speech in Leeds. In the speech he claimed Bradford was an Israeli-free area.
The spokesman added: "George is badly bruised but OK. He has bruising to his head and face and is in a pretty bad shape."
A Metropolitan Police spokesman said last night: "Police were called at approximately 19.40 hours this evening to Golborne Road, W10, after a man was assaulted in the street.
"Officers attended. The suspect was found a short time later and stopped.
"He was arrested on suspicion of actual bodily harm and taken to the south London police station where he remains."