The NCAA is made up of 1,100 colleges and universities in all 50 states that collectively enrol more than 530,000 student-athletes.
Mr Baker told a Senate committee in December that there were “less than 10” transgender athletes in the NCAA.
The new policy does permit student-athletes assigned male at birth to practice with women’s teams and receive benefits like medical care, but they are not allowed to compete.
Under Trump’s executive order, the education department has been directed to investigate schools for non-compliance.
Those found in violation could potentially be violating Title IX, the federal law that bans sex discrimination in schools.
“From now on, women’s sports will be only for women,” Trump said after signing the order on Wednesday.
Supporters of the order say it restores fairness to sports but LGBT advocacy and human rights organisations have described the move as discriminatory.
On Thursday, the education department announced an investigation into three schools “for suspected Title IX violations”.
Two colleges are suspected of allowing transgender athletes to compete in women’s sports after having been notified of Title IX changes – San Jose State University, the University of Pennsylvania, and the Massachusetts Interscholastic Athletic Association.
The NCAA’s eligibility policy for transgender athletes was last updated by the Board of Governors, external in January 2022.
That policy was described as a “sport-by-sport approach” aligning transgender student-athlete participation with the policies of the United States Olympic Paralympic Committee and International Olympic Committee.
Responding to the NCAA’s announcement, Republican Congressman Andy Ogle lauded the move, saying on X: “No more biological men in women’s sports.”
Nancy Armour, a sports columnist with USA Today, said the sports body “has lost its common sense, along with its spine”, and noted there have been longstanding policies at organisations like the NCAA allowing for transgender participation.
BBC News