Sarwan injured a joint in his right shoulder while falling awkwardly trying to prevent a boundary on the first day of the second Test on Friday.
"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," team manager Mike Findlay said on Tuesday from the team hotel in Leeds.
"The selectors are in discussions and a replacement for Sarwan is being sought and as soon as a decision is reached we will make an announcement on who the player is."
Sarwan was captaining the side for only the second time since taking over from Brian Lara after West Indies's disappointing World Cup campaign as hosts.
He was unable to bat against England as the tourists lost by a record innings and 283 runs at Headingley to go 1-0 down halfway through the four-Test series.
Sarwan will miss the remaining two Tests, three one-day internationals and two Twenty20 matches and leaves his side desperately short of top-quality batsmen.
"I am very disappointed that I will not be able to continue," Sarwan told the West Indies Cricket Board Web site.
"I have spoken to the players and wished them well for the remainder of the Tests, the Twenty20 series and the one-dayers.
"I have every confidence that the boys will be able to rebound after the defeat at Headingley."
The third Test, at Old Trafford, Manchester, starts on June 7.
