The Metropolitan Police confirmed a man was in custody over allegations dating back to between 2002 and 2009.
The Conservative Party said he had been asked by the chief whip not to attend Parliament while an investigation is ongoing.
The man also faces allegations of an abuse of position of trust and misconduct in a public office.
A Met Police spokesman would not confirm the identity of the man or if he was an MP, but published a statement, saying: "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."
He added: "A man... was arrested on suspicion of indecent assault, sexual assault, rape, abuse of position of trust and misconduct in public office."
The Conservative Whips office, which is responsible for party discipline, confirmed they had asked the MP to stay away from Parliament amid the investigation.
The office's spokesperson said: "The Chief Whip has asked that the MP concerned does not attend the Parliamentary Estate while an investigation is ongoing. Until the conclusion of the investigation we will not be commenting further."
The Met said the investigation was ongoing and being led by officers from the Central Specialist Crime unit.