The 24-year-old received a five-minute major and a game misconduct for the hit from behind on Letang. He was also penalized earlier in the game for cross-checking.
Letang stayed down on the ice, but was able to eventually skate off with a member of the training staff. He did not return to the game.
Rinaldo was recently charged with a game misconduct in Saturday's 4-0 loss to the Vancouver Canucks.
He is considered a repeat offender. Last season, Rinaldo sat out for four games for an illegal hit to the head of Buffalo Sabres' Chad Ruhwedel.