Multiple Swedish media sources, including newspapers such as Aftonbladet and Expressen, as well as public broadcaster SVT, have reported Mbappe as the suspect in the case.
"My assessment is that the evidence is not sufficient to proceed and the investigation is therefore closed," prosecutor Marina Chirakova said in a statement that also did not mention Mbappe by name.
Chirakova said the person in question had not been interrogated and "not been notified of suspicion of a crime".
"I have concluded, based on what has emerged in the case, that new evidence, including interrogations of the person in question, would not change the evidence situation right now," she told AFP.
She said her team had nonetheless "conducted a large number of interviews in the investigation".
Petra Eklund, the lawyer for the complainant, whose name has not been disclosed, told AFP she had "no comment" to the news that the case had been closed.
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Mbappe's lawyer said in October that he was "shocked" to see his name linked to the investigation.
Speaking for the first time about the case on Sunday, he told French television show Clique he was "not involved".
"I haven't received anything, no summons... I'm not involved," he said.
According to Aftonbladet, Mbappe and his entourage dined at a restaurant one evening before going on to a nightclub.
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The complaint was filed on October 12 after the alleged victim had sought medical attention, according to the newspaper.
Expressen reported that police had seized some clothing as evidence, saying it consisted of women's underwear, a pair of black trousers and a black top. Photographs showed police officers leaving the hotel with brown bags.
Difficult season
Mbappe joined Madrid this summer after seven years at Paris Saint-Germain and has stayed clear of scandal in his private life.
The forward, who is known for carefully managing his image through a close network of family, lawyers and spokespeople, has become one of the world's highest paid players after a stellar career that began when he was barely into his teens.
He has had a difficult season since moving to reigning European champions Real Madrid from PSG in the summer, failing to find his top form.
However the Frenchman scored in Madrid's 3-2 win against Italian side Atalanta on Tuesday which revived Real's flagging bid to regain their Champions League title.
Mbappe, Vinicius Junior and Jude Bellingham were all on the scoresheet in Bergamo as Madrid moved up to 20th place in the Champions League table, on nine points from six matches.
The Spanish giants would have been at risk of dropping out of the Champions League play-off places if they had lost.
Mbappe won the World Cup as a teenager in 2018 in Russia and scored a hat-trick in the 2022 final in Qatar which France lost on penalties to Lionel Messi's Argentina.
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At PSG he was part of a superstar trio with Messi and Brazilian forward Neymar, but the Qatar-owned club were unable to win the Champions League.
(Except for the headline, this story has not been edited by staff and is published from a syndicated feed.)