Christian Porter will no longer be attorney general but will remain in cabinet in a new portfolio.
Mr Porter has strongly rejected an allegation that he raped a girl in 1988 when he was 17.
Mr Morrison promoted several female lawmakers as part of a broader cabinet reshuffle on Monday.
The prime minister has faced intense pressure in recent weeks to respond to a series of rape, misconduct and sexism allegations which have rocked Australian politics.
Mr Porter will be replaced as attorney general and industrial relations minister by Michaelia Cash. He has been allocated the science and technology portfolio.
On Monday, Mr Porter said he had to be replaced as attorney general after commencing a defamation lawsuit against the ABC.
"[This] does not change anything in respect of the crucial principle that required me to instigate defamation proceedings," he said in a statement.
Another senior minister who has faced criticism - Linda Reynolds - was removed from the defence portfolio, but she will also remain in cabinet as government services minister.