Jacobs has returned to his native Antigua and will be replaced by Carlton Baugh, who made his debut in the second Test in Trinidad, the West Indies Cricket Board said.
The 35-year-old Jacobs missed the Trinidad Test because of a groin strain but was expected to play at the Kensington Oval.
The West Indies selectors also axed their most experienced fast bowler, Mervyn Dillon, and batsman Marlon Samuels.
The 27-year-old Dillon, who has taken 117 Test wickets in 32 appearances at an average of 31.86, has been dropped after taking only five wickets for 325
runs in the first two matches.
Fast bowler Tino Best and off-spinner Omari Banks will make their Test debuts in the match, which starts later on Thursday.
The 21-year-old Best, from Barbados, was called up following his impressive performances in the regional competition, where he claimed 39 wickets at an average of 18.25.
Banks, 20, will be the first player from the tiny island of Anguilla to play for the West Indies.
Australia lead the four-Test series 2-0.
Team: Brian Lara (captain), Ramnaresh Sarwan, Chris Gayle, Devon Smith, Daren Ganga, Shivnarine Chanderpaul, Omari Banks, Carlton Baugh, Vasbert Drakes, Jermaine Lawson, Tino Best.
