The test results were consistent with what law enforcement officials have said about the account provided by the woman, The New York Times reported, citing a person briefed in the matter.
The Wall Street Journal also reported that tests matched Strauss-Khan's DNA sample and semen found on the woman's shirt, citing law enforcement officials.
Other test results, including ones on samples taken from the carpet in the hotel suite, were pending, The New York Times said.
Both newspapers said Strauss-Kahn's lead attorney, Benjamin Brafman, had declined to comment.
Asked about the reported DNA results, York Police Department spokesman Paul Browne said: "Experienced NYPD detectives found the complainant's account credible from the outset, and nothing since then has changed their minds."
Strauss-Kahn is facing charges of sexual assault and attempting to rape the maid at the Sofitel hotel in New York on May 14. He is being held in an apartment in Manhattan under armed guard after being freed on bail on Friday.
In a letter to IMF staff circulated on Monday, Strauss-Kahn strongly denied charges against him and called the events around his arrest "a personal nightmare."
In the letter distributed to the fund's staff in an email by IMF acting Managing Director John Lipsky, Strauss-Kahn apologized for the pain his case had caused the global lender and said he was confident he would eventually be exonerated.
The letter reflects on his arrival at the fund in 2007 and explains his reasoning behind his resignation on Wednesday.
"I deny in the strongest possible terms the allegations which I now face; I am confident that the truth will come out and I will be exonerated," he said. A copy of the letter was obtained by Reuters.
(Reporting by JoAnne Allen, Michelle Nichols and Lesley Wroughton, editing by Christopher Wilson)