Hill was placed on the 10-day IL with a bruised rib cage, and Baddoo was placed on the seven-day concussion IL.
Tigers manager A.J. Hinch said Baddoo is dealing with some pain in addition to his concussion diagnosis.
"He feels like he was in a car crash," Hinch said. "It's a concussion with a pretty significant body soreness."
Hill and Baddoo both took off after Anthony Santander's drive to left-center field in the eighth inning. Each player reached for the ball -- and then they collided, sending Baddoo's cap flying.
"It was a nasty collision. It was a ball hit probably in the perfect spot for both guys to be going full speed, and both with a chance to catch it," Hinch said after his team's 9-4 win. "You don't see it a lot at this level. When you see them, they're nasty."
Hill did make the catch, but both outfielders left the game, able to walk off the field after a short delay.
The Associated Press contributed to this report.