This article is more than
1 year oldThe summons alleges that the plaintiff was assaulted by Mr Adams in 1993 "while they both worked for the City of New York".
A City Hall spokesperson said Mr Adams did not recall meeting his accuser and "vigorously denies" the claims.
The legal action was filed under New York state's Adult Survivors Act, which expires on Friday.
The state law created a year-long window for survivors of sexual misconduct to bring lawsuits that would otherwise have been blocked under the statute of limitations.
Former president Donald Trump and disgraced film producer Harvey Weinstein are among those who have been sued under the act.
An attorney for the plaintiff hailed the importance of the legislation, which they said has "given so many women the opportunity to seek justice".
The three-page summons contained few details about the alleged assault, but said the filing related to "intentional and negligent acts and omissions for physical, psychological, and other injuries suffered as a result of conduct that would constitute sexual offenses".
The woman is seeking $5m (£3.9m) in damages, the document added.
At the time of the allegations, Mr Adams was working as a police officer in New York City, and the summons also names the department's transit bureau as a defendant.
A social organisation for officers, called the Guardians Association, was also named.
In a statement issued on Thursday morning, a City Hall spokesperson said: "The mayor does not know who this person is. If they ever met, he doesn't recall it.
"But he would never do anything to physically harm another person and vigorously denies any such claim."
The summons is the latest legal blow for Mr Adams, a Democrat, who is also facing an investigation into the financing of his 2021 mayoral campaign.
Earlier this month FBI agents raided his apartment and seized three electronic devices, believed to be two iPhones and an iPad.
The raid followed a similar one on the Brooklyn residence of Brianna Suggs, 25, a lobbyist and former Adams aide.
The probe centres on whether his campaign conspired with the Turkish government to receive illegal foreign donations. Investigators want to know if the Adams campaign kicked back any benefits to the country or individuals in exchange for donations, according to a search warrant obtained by the New York Times.
Mr Adams has insisted he had no knowledge of any wrongdoing.
<p>A US judge has ruled against Donald Trump getting his hush money conviction thrown out on immunity grounds.</p>