Sarwan injured himself while chasing a ball to the boundary on the first day of the second Test against England here at Headingley and fell heavily on his right shoulder.
Sarwan was unable to bat in either innings as West Indies were beaten by an innings and 283 runs - their largest Test innings defeat of all-time.
"Unfortunately Sarwan's injury will take approximately six weeks to heal and as a result he will not be able to take any further part in this tour," Findlay said here on Tuesday at the squad's hotel.
Sarwan said: "I am very disappointed that I would not be able to continue on tour. But I have spoken with the players and wished them well for the remainder of the Test series and the Twenty20 games and the One-Day Internationals."
"I have confidence that the boys will be able to rebound after the defeat at Headingley and give a better account of themselves and the team as a whole," he added. Sarwan will leave London for the Caribbean on Wednesday.
West Indies, who are trailing 1-0 in the four Test series, have one warm-up game against MCC before the third Test starts at Old Trafford on June 7.
Their tour also features two Twenty20s, at the end of June, and three one-dayers, in July.
No decision has yet been taken on either a replacement skipper, although vice-captain Daren Ganga appears to be the leading candidate to take over, or a new batsman to replace Sarwan.
"As soon as a decision is reached we will make an announcement," said Findlay.
The 26-year-old Sarwan was in his first tour as captain after replacing Brian Lara who retired after hosts West Indies failed to reach the semi-finals of the World Cup in the Caribbean.