The guard suffered the injury during the final quarter of Tuesday's victory against the Detroit Pistons, having played 16 minutes and put up five points.
The Wizards confirmed Wright would undergo reassessment on the injury in mid-November, though reports from ESPN suggested he could be out for at least six to eight weeks.
"Delon Wright will be out indefinitely with a grade two strain of his right hamstring," the Wizards said in a statement.
"Wright suffered the injury in the fourth quarter of Tuesday’s game vs. Detroit. He will be re-evaluated in approximately three weeks."
The 30-year-old arrived as a free agent in the off-season, having spent last campaign with the Atlanta Hawks.