Sarwan was ruled out of the rest of the series with a shoulder injury incurred in the innings defeat to England at Headingley last week.
Having only taken over the captaincy last month from the retired Brian Lara, he is likely to be sidelined for six weeks.
The tour vice-captain, Ganga, 28, effectively led the Windies during the second Test loss which left the tourists 1-0 down in the four-match series after Sarwan fell heavily on the first evening.
He has experience of captaincy, having impressed in charge of the West Indies' A side over the last couple of years and he was one of the candidates to succeed Lara.
Middle-order batsman Shivnarine Chanderpaul, meanwhile, is expected to be fit to play at Old Trafford on Thursday after missing the match in Leeds due to tendinitis in his knee.