The move means he will not be an SNP MP at Westminster.
The Sunday Times and the Sunday Mail first reported that officers from the Met Police would be making further inquiries into allegations against him.
Nicola Sturgeon and the SNP Westminster leader have faced questions over the way the allegations were handled.
The Glasgow North MP, who will sit as an independent, was suspended from parliament for two days after he was found to have made a sexual advance to a teenage SNP member of staff.
Mr Grady, the party's former chief whip, told the Commons he was "profoundly sorry" after an independent panel found he had touched and stroked the neck, hair and back of his colleague during a social event at a London pub in 2016.
A spokesman for the Metropolitan Police said: "On Wednesday, 22 June police received an allegation of sexual assault that is said to have taken place in October 2016 at a commercial premises in Folgate Street, E1.
"The report was submitted online by a third party.
"Officers will now be making inquiries, including contacting the alleged victim, in order to assess what further action is required."
An SNP spokesman said: "Patrick Grady is stepping away from his party membership while the police inquiry continues."
Last week, First Minister Nicola Sturgeon said the SNP's Westminster group had questions to answer over its handling of the harassment complaint against Mr Grady.
Ms Sturgeon said she still had confidence in her party's Westminster leader Ian Blackford but said a victim who did not feel supported "is by definition unsupported".
After it was recommended that Mr Grady was suspended from parliament for two days, it emerged that Mr Blackford had subsequently urged his party's MPs to "give as much support as possible" to the MP after audio of an SNP group meeting was leaked to the Daily Mail.
Mr Grady's victim told BBC Scotland on Thursday that the party was closing ranks and attempting to discredit him in order to limit the fallout from the case, and was more interested in finding the source of the leaked audio than addressing the issues that it raised.
He dismissed Mr Blackford's apology over what was said at the group meeting and his "regret" that the victim felt unsupported as a "cop out" and a "publicity stunt" that was done to protect the politician's position and reputation.
In response, Mr Blackford said he was willing to meet the victim, adding: "If the complainant feels aggrieved, then I am sorry for that."
He said he had not yet had an opportunity to apologise in person because the investigation process had only just concluded, and said he also had a duty of "pastoral care" to Mr Grady.
He said he "regrets the fact the discussion took place the way it did" during the SNP group meeting, but denied his authority had been undermined by the situation. Mr Blackford also refused to directly call for Mr Grady to stand down but suggested he needed to "reflect on his behaviour".
Scottish Conservative chairman Craig Hoy MSP said: "Patrick Grady should have been sacked long before this but the SNP have shown they have absolutely no backbone and would rather back the perpetrator over the victim.
"The abuser is gone but the poison remains in the SNP and the party leadership should be ashamed of the way they have handled this scandal.
"It's appalling that Nicola Sturgeon and Ian Blackford are still treating a disgraced MP with more sympathy than the victim who suffered sexual harassment."
Mr Hoy also called for Ian Blackford to be sacked "so victims have confidence that they'll be taken seriously in the future".
Scottish Liberal Democrat leader Alex Cole-Hamilton also called for Mr Blackford's resignation.
He said: "At no point has Ian Blackford showed an ounce of leadership. He voiced absolute full support for Patrick Grady over the victim, allowed SNP whips to act menacingly and resorted to intimidation," he said. "Ian Blackford must go."
It's not clear if Patrick Grady had much choice in "stepping away" from the SNP but the party has certainly given the impression that it was his decision.
By excluding himself from membership at a time when the party has begun the selection process for the next general election, Mr Grady may, in effect, be excluding himself as a candidate and ending his parliamentary career.
That may depend firstly on how long the police process takes and - if it is reasonably swift - whether or not they decide to take any action.
This is not the only follow-up to this story because while Nicola Sturgeon has expressed confidence in her Westminster leader Ian Blackford, she has also questioned his handling of the case.
She has also offered to meet face to face with the SNP staff member who was touched inappropriately by Patrick Grady. He has yet to decide whether or not to accept her invitation.
This is hardly the curtain raiser the first minister would have wanted for her Holyrood statement on Tuesday on how she plans to bring about an independence referendum in October next year.