Fleener (right) and quarterback Andrew Luck (left) in their NFL debuts in 2012.
The Indianapolis Colts made Fleener the 34th overall selection in the 2012 NFL Draft after drafting his college quarterback, Andrew Luck, 1st overall. Fleener was the first tight end drafted in the 2012 NFL draft. On July 25, he and the Colts agreed to a 4 year contract worth $5.431 million.
Fleener made his regular season debut in Week 1 against the Chicago Bears, making 6 receptions for 82 yards. He would struggle through the early season, before recording his first touchdown reception against the Detroit Lions in Week 13. Fleener finished the 2012 regular season with 26 receptions for 281 yards and 2 touchdowns. He recorded 3 receptions for 25 yards in the Colts Wild Card loss to the Baltimore Ravens.
Fleener began the 2013 preseason as the backup to Dwayne Allen. He missed the final two weeks of preseason after suffering a knee injury. Allen would be placed on injured reserve after Week 1, making Fleener the starter for the rest of the season. He recorded his first 100 yard receiving game in Week 11 against the Tennessee Titans, making 8 receptions for 107 yards. Fleener finished the 2013 season with 52 receptions for 608 yards and 4 touchdowns. In the Colts Wild Card playoff game against the Kansas City Chiefs, he would have 5 reception for 46 yards and a touchdown to assist in the Colts' 45-44 comeback win.