Happ is day-to-day with a rib contusion and won't go through concussion protocol, Cubs manager David Ross said, according to the Chicago Tribune's Meghan Montemurro.
The 26-year-old will undergo additional tests with Cubs trainers Tuesday, Montemurro adds.
Happ is off to a rough start in Chicago, hitting .167/.307/.250 with 14 hits in 26 games after receiving down-ballot MVP votes in 2020.
Meanwhile, Hoerner was placed on the 10-day injured list with a left forearm strain, the team announced. The 23-year-old owns a .389/.500/.556 slash line with seven RBIs and three steals in 11 games.
"Scariest baseball play I've been a part of," Hoerner said of the collision, according to NBC Sports Chicago's Gordon Wittenmyer.
"All things considered, both pretty fortunate where we're at and especially for his head to be in good shape after something like that was the biggest concern for everyone."
Left-hander Kyle Ryan, right-hander Keegan Thompson, and infielder Ildemaro Vargas were added to the big-league roster in corresponding moves.