Mr Galloway was posing for pictures with people in Golborne Road, Notting Hill, London, when a man shouted a comment about the Holocaust and laid into him.
Police were quickly on the scene and made an arrest.
Mr Galloway was making a statement at Notting Hill Police Station, the spokesman said.
The 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."
The spokesman had no idea whether the attacker was an Israeli, an EDL-supporter or had some other motivation for attacking the Bradford West MP.
Mr Galloway was interviewed earlier this month by West Yorkshire Police following a speech in Leeds in which 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: "Police were called at approximately 1940 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 ABH and taken to the south London police station where he remains."
In 2008 Mr Galloway was pelted with a rubber stress ball as he was campaigning in an open-top bus in London.
The firebrand politician received medical treatment but was not taken to hospital.
A man was arrested and cautioned by police over the incident.