If a major league player cannot play because of a medical condition, he may be placed on the 15-day or 60-day disabled list. The team then frees up a spot on its active and/or 40 man roster, and the player may not play for at the duration of their disabled list status.
In baseball, if the injured player is a pitcher, the replacement pitcher gets as much time as necessary to warm up. Injured player, once removed from the game, cannot return.