A message on Luton councillor Aysegul Gurbuz's Twitter feed claimed Hitler was the "greatest man in history".
Another tweet on Gurbaz's account suggested Iran could develop a nuclear weapon to "wipe Israel off the map", the BBC reported.
Gurbuz, who is Muslim, became Luton's youngest councillor when she, a student, was elected to the High Town ward last year.
Labour leader Jeremy Corbyn said anyone who makes anti- Semitic remarks is "auto-excluded from the party" pending an inquiry.
The Labour Party has confirmed she has been suspended pending an investigation.
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"We have suspended, we will suspend, any member that behaves in that way."
The tweets in question were made before Gurbuz was elected to Luton Borough Council in May 2015.
A spokesman for the council said: "While these comments appear to pre-date her time as a councillor, the council is shocked by these comments.
"This matter will be referred as a matter of urgency to the council's independent standards committee to allow a full investigation to take place."
On Thursday, Corbyn was criticised by a Jewish leader for not taking anti-Semitism seriously enough.