Cotterell was forced to pull out of the tour after suffering from pain in his left knee Wednesday, reports CMC.
"It was a devastating blow when we found out that Sheldon was injured and could not play. He is one of the most promising quick bowlers we have in the West Indies," team manager Lockhart Sebastien said.
"We were looking forward to seeing him perform well on this tour for the West Indies A team, but unfortunately he has been ruled out due to injury."
Cotterrell was named in both the limited-overs and four-day squads but did not play any of the three one-dayers or the one-off T20.
He was not in the XI for the first unofficial Test set to enter its second day in Mysore Thursday.
"He was impressive in recent months, especially in the Caribbean Premier League (CPL) and this was a great chance for him to show his skills again," said Sebastien.
"We are still confident we have the bowlers to do the job and we expect the team to continue doing well on this tour."
Edwards last played for the West Indies during the tour of Bangladesh late last year.
He didn't feature in the West Indies' home international season this year but played the CPL, in which he took nine wickets, including a five-wicket haul.