David Laverick, chairman of the Adjudication Panel for England, the disciplinary panel which ruled on the case, said: "His treatment of the journalist was unnecessarily insensitive and offensive."
The suspension is effective from 1 March.
Livingstone has the right to appeal against Friday's ruling.
Tony Child, a lawyer for the mayor, said: "This is extremely disappointing. We will be considering our right to appeal to the High Court."
Since Livingstone lost the case he must pay his own costs, estimated at more than ?80,000 ($175,000).
The panel made no recommendation whether his salary should be suspended.
Laverick said the panel was concerned that Livingstone refused to apologise and was in breach of the Greater London Authority code of conduct.
He said: "The mayor does seem to have failed, from the outset of this case, to have appreciated that his conduct was unacceptable, was a breach of the code and did damage to the reputation of his office.
"His representative is quite right in saying, as he did on 23 February, that matters should not have got as far as this but it is the mayor who must take responsibility for this."
Livingstone did not attend Friday's session to hear the ruling.
The mayor had told the panel he had not meant to offend the Jewish community when he asked Evening Standard reporter Oliver Finegold whether he had been a "German war criminal".
"There's a right to be offensive and to express in hyperbolic terms opposition to Associated Newspapers and their policies"
Ken Livingstone's lawyer
Finegold, who had approached the mayor for comment after a reception for the gay and lesbian community in February, replied that he was Jewish.
Livingstone told the reporter he was "just like a concentration camp guard. You're just doing it because you're paid to, aren't you?"
He referred to Finegold's employer as "a load of scumbags and reactionary bigots".
That was a reference to Associated Newspapers, publishers of the Evening Standard, the Daily Mail and the Mail on Sunday.
Child said: "The whole point being made was a dislike for Associated Newspapers and their history of supporting policies which are inconsistent with the policies of the mayor.
"There's a right to be offensive and to express in hyperbolic terms opposition to Associated Newspapers and their policies."
Livingstone has also pointed to the pro-Nazi line taken by the Mail papers in the 1930s.
Veronica Wadley, editor of the Evening Standard, said: "This paper has not always seen eye to eye with Mr Livingstone.
"We believe, though, that it is only right that the adjudication panel has now decided that Mr Livingstone acted in a manner that was ill-fitting for the mayor."