Wightman, who stormed to a memorable 1,500m gold medal at the 2022 World Championships, had been due to compete in the 800m in Paris.
The 30-year-old Scot will be replaced by Elliot Giles, Team GB said in a statement.
Wightman has struggled to return to the peak form that saw him take gold at the World Championships in Eugene, Oregon two years ago.
A torn calf muscle ruled him out of the British trials but he was handed a discretionary place on the team for Paris in the 800m before being ruled out on Thursday.