Per Tim Kelly of Phillies Nation, Alvarez had to be carted off the field after a liner from Lourdes Gurriel Jr. hit him in the groin. Alvarez was able to throw Gurriel out before falling to the ground.
Per MLB.com's Todd Zolecki, the ball came off Gurriel's bat at 105.3 mph.
Zolecki noted the Phillies didn't have an immediate update on Alvarez's status after Toronto's 3-2 victory.
Rookie Spencer Howard reached his pitch limit after 3.2 innings and was replaced by Blake Parker in the fourth. Alvarez took over for Parker with two outs in the bottom of the fifth.
Philadelphia's bullpen has been a problem in 2020. The group had an 8.11 ERA with 90 hits allowed in 61 innings coming into Thursday's games. Seranthony Dominguez will miss the entire season after having Tommy John surgery in July.
David Robertson (elbow) and Ranger Suarez (COVID-19) are still working their way back.
Alvarez has been one of the few bright spots for the Phillies bullpen. The left-hander has a 1.42 ERA with six strikeouts in 6.1 innings.