"He will struggle to make the playing eleven, but we will continue to monitor his situation," India captain Rahul Dravid said after his team's 116-run win over Jamaica on Tuesday.
Team physiotherapist John Gloster was hopeful the portly Powar will be available for the remaining four One-dayers.
"Powar has a right ankle ligament strain, but the good thing is there is no fracture," said Gloster.
Powar, with 12 wickets in 11 one-dayers, sustained the injury during Monday's training session and did not play the practice game the next day.
Meanwhile, seamer Shanthakumaran Sreesanth was also a doubtful starter for Thursday as he had not recovered fully from the ankle injury suffered during the two One-dayers against Pakistan in Abu Dhabi last month.
"Sreesanth's condition will be monitored regularly," said Dravid.
India, looking for their first Test series win in the Caribbean in 35 years, will play four Test matches after the one-day series.