The unnamed man in his 50s was arrested on Tuesday over allegations dating back to between 2002 and 2009.
He has been released on bail to a date in mid-June pending further enquiries.
Labour is calling on the Conservatives to suspend the man from the parliamentary party, meaning his identity would become public.
A spokesman for Labour leader Sir Keir Starmer said it was a "matter for the Conservative Party" but that the "nature of the allegations" meant it "doesn't seem to be sustainable to argue that he shouldn't be suspended from the whip".
The spokesman added that removing the whip would "inevitably" mean the individual would be named publicly.
He confirmed that Sir Keir would suspend a Labour MP if they were facing the same allegations.
The man is not being named by media outlets.
The police do not usually name individuals until they are charged and Parliament is not required to identify MPs who've been arrested.
Earlier this year, the Supreme Court strengthened the right to privacy for people who are under investigation but have not been charged.
A spokeswoman for Prime Minister Boris Johnson said the vast majority of MPs behaved appropriately, but added the behaviour of a minority was "not acceptable".
In a Commons statement, Sir Lindsay Hoyle said he took "the safety of our staff and parliamentary community as a whole very seriously".
Sir Lindsay also warned MPs against naming the individual in the Commons chamber, saying he believed it would be "wholly inappropriate for any further reference to be made to this matter in the House".
The Conservatives confirmed on Tuesday that their chief whip had asked the MP to stay away from the parliamentary estate during the police inquiry.
Labour's shadow Home Office minister Jess Phillips said there were difficulties about an individual being named.
"If I was a constituent in this MP's or any of the previous cases of MPs' constituencies, I might feel I had a right to know.
"Because there's nothing that can stop them seeing their constituents completely in private, completely on their own...I might want to empower myself to make that decision.
"But that is a finely balanced thing and what you don't want is trial by media."
In a statement on Wednesday, the Met said: "In January 2020, the Met received a report relating to alleged sexual offences having been committed between 2002 and 2009.
"The offences are alleged to have occurred in London.
"An investigation is ongoing, led by officers from Central Specialist Crime.
"A man, aged in his 50s, was arrested on suspicion of indecent assault, sexual assault, rape, abuse of position of trust and misconduct in public office.
"He was taken into custody and has since been bailed pending further enquiries to a date in mid-June."