The Colts signed Griffey as an undrafted free agent on May 4. He had 79 catches for 1,241 yards and six scores in 44 games at Arizona before joining the NFL franchise.
Griffey participated in the Colts' three-day rookie mini-camp.
The wide receiver was an All-PAC 12 honorable mention selection last season. He is listed at 6-foot, 3-inches and 192 pounds.
The Colts signed free agent wide receiver Chris Briggs in a corresponding move. Briggs had 11 catches for 168 yards and two scores in 10 games in 2015 for Southeastern Louisiana. The Seattle Seahawks waived Briggs on May 9.
Griffey can be cut from injured reserve when healed and can negotiate an injury settlement, noted Pro Football Talk.
The Colts did not take any wide receivers in the 2017 NFL Draft, but have T.Y. Hilton, Donte Moncrief and Phillip Dorsett on its roster. Griffey was also drafted in the 24th round of the 2016 MLB amateur draft by the Seattle Mariners.
The elder Griffey was inducted into the Baseball Hall of Fame in 2016. He played 13 seasons for the Mariners. The Griffey's lived in Indianapolis for a short time, when Ken Griffey Sr. played for the Indianapolis Indians in the 1970s.
The Colts have mandatory minicamp from Tuesday through Thursday.