The 25-year-old French star, one of the highest-profile players in world football, visited the Swedish capital October 9-11 with a group of people after he was not selected by his country for a Nations League match.
Sweden's prosecution authority announced on October 15 that it was investigating an alleged incident that occurred at an upscale Stockholm hotel on October 10, without mentioning the suspect by name.
Several Swedish media outlets, including newspapers Aftonbladet and Expressen and public broadcaster SVT, identified Mbappé as the suspect.
"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 Mbappé by name.
Chirakova said the suspect had "not been notified of suspicion of a crime".
Mbappé'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.
Aftonbladet said the Mbappé was filed on October 12 after the alleged victim had sought medical attention.
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.
Mbappé has had a difficult season since moving to reigning European champions Real Madrid from Paris Saint-Germain 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.
Mbappé , 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.
Mbappé is one of the hottest properties in world football.
He 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.
At Paris Saint-Germain he was part of a superstar trio with Messi and Brazilian forward Neymar.
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