The Equalities and Human Rights Commission (EHRC) said it was examining a number of allegations and had asked Labour for a response.
In a statement, an EHRC spokesman said: "Having received a number of complaints regarding anti-Semitism in the Labour Party, we believe Labour may have unlawfully discriminated against people because of their ethnicity and religious beliefs.
"Our concerns are sufficient for us to consider using our statutory enforcement powers.
It comes as the Labour’s main Jewish group gave the party leadership a month to act on concerns after voting against breaking away after 100 years of affiliation.
In a further deepening of divisions over the party’s antisemitism crisis, Labour MPs who failed to sign a pledge of solidarity with the Jewish Labour Movement (JLM) were accused of "moral cowardice" by one of their parliamentary colleagues, while another likened the problem to "fascism".
Hundreds of JLM members gathered at a synagogue in central London on Wednesday night, with another meeting taking place in Manchester.
JLM national secretary Peter Mason said members had backed retaining their affiliation with Labour, which dates back to 1920.
"We had an indicative vote this evening that we will stay, we will stand and we will fight against anti-Semitism in the Labour Party," he said.
"The message from the Jewish Labour Movement this evening was absolutely clear.
"If the Labour Party fails to show solidarity to us, we will not show solidarity to it.
"That counts for MPs who do not sign their names to letters showing solidarity with us, that counts for members of the Scottish Parliament, that counts for councillors."
He added: "It is very clear: we have set the tests that the leadership need to meet and we expect them to do that before our AGM on April 7."
The JLM said it had made a submission to the Equalities and Human Rights Commission in November last year, asking it to investigate the allegation that the Labour Party was institutionally anti-Semitic.
A spokesman said: "We did not take that decision lightly... This evening Jewish Labour members made clear that we will not unconditionally stand by whilst we are treated with such intolerance and contempt.
"We, in our history, have loved and respected the Labour Party too much to let this continue."
He hit out at colleagues for failing to sign up to a letter organised by fellow MP Stella Creasy expressing solidarity with Jewish members.
"More than 100 Labour MPs signed a letter of solidarity with the Jewish Labour Movement. But where was the majority of my parliamentary colleagues and why are they showing such moral cowardice in the face of such pain from our Jewish members?
"They have a responsibility to step up as well."