The incident was reported to have happened in the Bon Accord Crescent area on Friday.
A report on the man, 20, was sent to the procurator fiscal.
The Crown Office said: "After full and careful consideration of the facts and circumstances of the case, he was liberated from custody pending further inquiries and did not appear in court."
A man charged after a 20-year-old woman was allegedly raped in Aberdeen has been freed.