The Metropolitan Police have launched the criminal investigation and are acting on a dossier of information handed to Commissioner Cressida Dick.
Ms Dick said officers were asssessing online material because “there may have been a crime committed”.
The investigation was sparked by an internal Labour Party dossier detailing 45 cases, involving messages posted by members of social media, obtained by radio station LBC.
One message is alleged to have said: “We shall rid the Jews who are a cancer on us all.”
A Met Police spokesman said: “On Tuesday September 4, the Met Commissioner was handed a folder of paperwork following a radio interview with LBC Radio in Leicester Square.
“The complainant alleged that the documentation included evidence of anti-Semitic hate crimes.
“The contents have been examined by specialist officers.
“A criminal investigation has commenced into some of the allegations within the documentation.
“Early investigative advice is being sought from the Crown Prosecution Service.
“The MPS will not comment further on the details of our investigation.”
Met Police Commissioner Ms Dick insisted the the Labour Party itself was not under investigation.
The investigation was launched after LBC handed the dossier to Ms Dick during an interview in September, according to the BBC.
LBC said allegations included threats against MPs, including a Faecbook message that a female Labour MP was a “zionist extremist who hates civilised people” and is “about to get a good kicking”.
Ms Dick said police had a “duty” to look at the evidence and “not just dismiss it”.
She told BBC Radio 4’s Today programme: “We are not going to investigate the Labour Party. We would always want institutions and political parties and similar to be able to regulate themselves.
“However, if somebody passes us material which they say amounts to a crime we have a duty to look at that and not just dismiss it.
“We have been assessing some material that was passed to me, in a radio studio of all things, about two months ago and we are now investigating some of that material because it appears there may have been crime committed.
“We are liaising immediately with the Crown Prosecution Service and I hope we will be able to clear that up very quickly.”
A Labour Party spokesman said they had not been contacted by the police but is ready to co-operate with the investigation.
He said: “The Labour Party has a robust system for investigating complaints of alleged breaches of Labour Party rules by its members.
“Where someone feels they have been a victim of crime, they should report it to the police in the usual way.”
Deputy Labour leader Tom Watson said Jeremy Corbyn’s Labour party was “determined to root out” anti-Semitism.
Speaking on BBC Radio Scotland, he said: “If it does one thing, it will dispel the myth that has been propagated by some people in my own party and beyond it that there is an anti-Semitism in my own party and we are determined to root it out.”
“I’ve not seen the details within the dossier, I just know it exists.
“I don’t know how it ended up in the hands of the police but I’m very pleased it has done because we’ve not just said that we want to root out anti-Semitism in the Labour Party, but if people have crossed the line on criminal behaviour through hate crime, and I’m afraid it doesn’t surprise me that some have, then I’m very pleased that this is being taken seriously by the police.”