By Agence France-Presse
No reason was given for the conservative jurist's decision to pull out but the announcement follows a petition for his ouster signed by hundreds of alumni.
Administrators at the prestigious college emailed students late Monday to say Kavanaugh "indicated that he can no longer commit to teaching his course in January Term 2019, so the course will not be offered."
A Harvard Law School spokesman confirmed that Kavanaugh would not return to teach.
The federal appeals court judge had taught the three-week course, entitled "The Supreme Court since 2005" at what is one of the most distinguished law schools in the United States, for around a decade.
An online letter, begun last Friday and on Tuesday morning signed by more than 860 Harvard Law School alumni, asked the college to rescind his appointment as lecturer and bar him from teaching.
"We believe that Judge Kavanaugh's appointment as an HLS lecturer sends a message to law students, and in particular female students, that powerful men are above the law," it says.
"Judge Kavanaugh is not leadership material and he is not lectureship material. HLS would be tarnished to have him on campus in any position of authority. We ask that you rescind his lectureship."
Three women say the conservative jurist drunkenly sexually abused or harassed them when they were students in the 1980s.
In an extraordinary Senate hearing last Thursday, Kavanaugh denied the abuse allegations and was adamant he did not drink to the point of blacking out, despite enjoying beer in his younger years
"In addition to the substance of these allegations, Judge Kavanaugh's comportment and testimony during the appointment process have cast further doubt on his fitness to serve on the Supreme Court," said the alumni letter.