Under Bailey's tenure, the Academy expelled Weinstein- who has consistently, through his spokesperson, denied any "non-consensual acts" and "acts of retaliation" - from its ranks and instituted a new "Standards of Conduct" to address sexual harassment and abuse claims.
"The Membership Committee reviews all complaints brought against Academy members according to our Standards of Conduct process, and after completing reviews, reports to the Board of Governors", the statement said.
The accusations against Bailey come less than two weeks after he oversaw his first Academy Awards ceremony as president.
It was unclear if Bailey would continue to serve as the president of the Academy or if he has been suspended during the investigation.
Bailey has worked in Hollywood for more than forty years, shooting such films as The Big Chill, Groundhog Day and How to Lose a Guy in 10 Days.
The investigation comes five months after The Academy kicked out Harvey Weinstein amid a wave of sexual harassment and assault allegations against him.
The standards outlined how the academy will approach sexual misconduct allegations going forward. Such evidence could include "1) the violation was witnessed by another; 2) the violation was reported to another, after the event occurred; 3) the violation was memorialized in writing after the incident occurred; 4) the violation is part of an established pattern by the same member; 5) following the violation, the claimant experienced verifiable changes in their mental, emotional or physical wellbeing".
Under the policy, the Academy's Membership and Administration Committee reviews allegations.
Bailey was elected as president of the prestigious organization, which is made up of 7,000-plus members of the film industry, in August 2017.
The Board of Governors sets the Academy's strategic vision, preserves the organization's financial health, and assures the fulfillment of its mission.
Bailey, 75, is in his first year as President of The Academy. Should the academy choose to let Bailey go, Lois Burwell, a veteran makeup artist, will fill the role until the next election in July.