The winger will not play Game 5 in Toronto, with Jesper Boqvist slotting into the lineup in his place, head coach Paul Maurice told reporters.
Rodrigues was forced out of Game 4 late in the third period after a check from Maple Leafs defenceman Oliver Ekman-Larsson appeared to injure him. Ekman-Larsson was initially assessed a five-minute major penalty, but the infraction was reduced to a two-minute interference minor upon review.
In nine playoff games, Rodrigues has registered three assists. He had 15 goals and 17 assists in 82 regular-season games.
Boqvist, 26, last played in Game 2 when he logged 5:40 of ice time against the Maple Leafs. In 78 regular-season games, he had 12 goals and matched a career-high 23 points.
You can watch Game 5 between the Panthers and Maple Leafs on Sportsnet and Sportsnet+ at 7 p.m. ET / 4 p.m. PT.