The Metropolitan Police had said they received allegations on 31 July of sexual offences and assault relating to four separate incidents at addresses in London, including in Westminster, between July last year and January this year.
A man was arrested on 1 August on suspicion of rape and was taken into custody at an east London police station before later being released on bail, the force added.
But a Metropolitan Police spokesperson said: “Following a thorough investigation, and based on all evidence made available to officers, the decision was taken that the case did not meet the evidential test and no further action will be taken.”
“The complainant has been made aware of the decision.”
The man, whom the Sunday Times reported has been carrying out parliamentary duties from home since his arrest, has been told of the police decision.
The alleged victim told the paper she intends to appeal against the decision under the Victims’ Right to Review Scheme.
Following the man’s arrest, housing secretary Robert Jenrick said on 2 August that he did not know the name of the MP.
Mr Jenrick added that parliament “needs to be” a safe environment for young women to work in.
He told Times Radio: “There have clearly been some very difficult allegations and cases in recent years.
“We need to make sure, like any other workplace, it is one that’s fit for everybody, where everybody feels safe and comfortable working, and when allegations are raised they are treated with the seriousness they deserve.”
Asked whether he personally wanted to see the Tory whip removed from the MP under police investigation, Mr Jenrick said: “We need to take allegations of this nature very seriously and I'm confident that the party is, and will do.”
Numerous reports in the Sunday papers on 2 August said the allegations were raised with Tory chief whip Mark Spencer, and the complainant also spoke to him, but no action was taken.
PA understands that Mr Spencer advised her to make a formal complaint to authorities who would be able to investigate the claims.
A spokesperson for Mr Spencer said: “The chief whip takes all allegations of harassment and abuse extremely seriously and has strongly encouraged anybody who has approached him to contact the appropriate authorities, including parliament’s independent complaints and grievance scheme, which can formally carry out independent and confidential investigations.”
A Conservative Party spokesperson said: “We take all allegations of this nature extremely seriously. As this matter is now in the hands of the police it would be inappropriate to comment further.”
The investigation came days after former Conservative MP Charlie Elphicke was convicted at Southwark Crown Court in a separate case of sexually assaulting two women, one of whom was a parliamentary worker.