According to Cleveland.com -- which first reported the injury -- the team's first-round draft pick broke a hand Wednesday when he caught a pass and someone came down it during practice.
Coleman, a former Baylor standout who was selected 15th by the Browns in this year's draft, had a strong game in Sunday's 25-20 loss against the Baltimore Ravens, catching five passes for 104 yards and two touchdowns.
Coleman's injury continues a streak of misfortune that is a lot for any team in two games -- even the Browns.
Defensive lineman Carl Nassib also had surgery to repair a broken bone in one of his hands and will miss at least this week. In the opener, Robert Griffin III broke the coracoid bone in his left shoulder and was placed on injured reserve.
Heading into the third game of the season Sunday in Miami, the Browns have lost two quarterbacks, their first-round pick (Coleman) and third-round pick (Nassib) to injury.
ESPN Browns reporter PatMcManamoncontributed to this report