The Canadian underwent surgery after a part of his car's suspension pierced both of his legs after he hit a wall.
It is a first IndyCar career pole for 29-year-old Hinchcliffe, who missed the rest of 2015 before returning for the start of the 2016 season in March.
Hinchcliffe won it on the final run of the nine-car pole shootout.
It was the fourth closest differential between first and second in the race's 100-year history.
Josef Newgarden will start from second in the race, to be held on 29 May in Indiana.