The group behind the Oscars launched an investigation after a claim against president John Bailey was received on March 13.
The claimant and details of the allegation were not made public by the Academy.
"The Membership and Administration Committee and its sub-committee thoroughly reviewed and considered the claim, John Bailey's response, and corroborating statements from both parties," the statement read. "The Academy took the claim very seriously and was cognizant of the rights of both the claimant and the accused, including consulting with outside counsel with expertise in matters related to harassment."
The cinematographer became president of the Academy in August 2017, after taking over the post from Cheryl Boone Isaacs.
Bailey started his term just before the Harvey Weinstein scandal broke, which has heightened attention to sexual misconduct in the entertainment industry.
Dozens of women have accused Weinstein of abuse, following reports in the New York Times and the New Yorker last year about his treatment of women, including some the mogul had worked with.
Weinstein has been accused of rape, assault and other forms of sexual misconduct, but has steadfastly denied via his rep "any allegations of nonconsensual sex."
"The Committee unanimously determined that no further action was merited on this matter," the Academy's statement on Bailey read. "The findings and recommendations of the committee were reported to the Board, which endorsed its recommendation."
Bailey remains president of the Academy.