"Shaun has a chronic, deep tendonitis injury caused by over-use and is taking a little bit longer to respond to treatment which is not uncommon with these types of injuries," South Africa physio Shane Jabaar said on Tuesday.
The United Cricket Board of South Africa (UCBSA) said in a statement that seam bowler Pollock would remain at home in Durban to undergo treatment and a rehabilitation programme.
"He will be monitored on a constant basis and should he show sufficient improvement and be able to bowl symptom-free, a decision on when he will join the tour will be taken at that time," Jabaar added.
The UCBSA has not named any replacement for Pollock.
Pollock has struggled with the injury since England's tour to South Africa earlier in the summer and he missed all three One-day Internationals and one of the two Tests South Africa played against touring Zimbabwe.
South Africa's other injury concerns yielded better news, with fast bowlers Charl Langeveldt and Andre Nel passing fitness tests on lower back and hamstring injuries respectively.
Jabaar said all-rounder Jacques Kallis was "80 per cent fit" following his hip injury.
South Africa leave for the Caribbean on Wednesday.