Fleener suffered the injury during the team's 44-20 preseason loss to the Buffalo Bills on Sunday. There has no been no definitive date set for his return.
The second-year man out of Stanford did attend practice, but watched from the sideline in street clothes as the team ran through its afternoon drills.
The Colts are also without tight end Dwayne Allen, who watched alongside Fleener in on crutches after injuring his right foot during practice last week.
Fleener had 26 receptions for 281 yards and two touchdowns during his 2012 rookie season.