The 20-year-old was selected by Chicago with the No. 17 pick in the 2020 draft. He made his NHL debut last season and recorded an assist in 11 games.
Sending Reichel back to Rockford puts him in position to play major minutes with the AHL team, instead of a smaller role with the rebuilding Blackhawks.
Forwards Mike Hardman, Cole Guttman, Michal Teply and Josiah Slavin and defensemen Isaak Phillips and Jakub Galvas also were assigned to Rockford. The moves dropped Chicago's training camp roster to 33 players.
Earlier this week, the team announced that forward Boris Katchouk would be sidelined four to six weeks because of a left ankle sprain. The 24-year-old Katchouk played almost 12 minutes during a 3-0 preseason loss to Detroit on Saturday night. He was acquired in a multiplayer trade with Tampa Bay in March.
The Blackhawks open the season Oct. 12 vs. the Colorado Avalanche.
The Associated Press contributed to this report.