An MRI confirmed Alzolay is dealing with a right flexor strain, Meghan Montemurro of the Chicago Tribune reports.
The Cubs placed Alzolay on the 15-day injured list Monday with a right forearm strain, Taylor McGregor of Marquee Sports Network reports.
Alzolay (1-4) allowed three runs on four hits while retiring just a single batter to take the loss Friday against the Brewers.
Cubs manager Craig Counsell indicated Sunday that Alzolay isn't currently the club's closer, and the skipper said he'll treat the role as a "day-to-day thing," Steve Greenberg of the Chicago Sun-Times reports.
Alzolay blew the save Tuesday against Arizona, allowing one run on one hit and two walks across one inning. He didn't generate a strikeout.
Alzolay earned the save in Friday's 9-7 win over the Dodgers, working around two hits in a scoreless inning.
Cubs manager Craig Counsell isn't ready to hand out defined roles for Alzolay or any other member of the bullpen, Sahadev Sharma of The Athletic reports.
Alzolay (illness) struck out one and worked around a base hit in a scoreless inning of relief Sunday in the Cubs' 5-3 win over the Guardians in Cactus League play.
Alzolay did not play in Friday's spring training game against the White Sox due to an illness, Maddie Lee of the Chicago Sun-Times reports.
Alzolay will likely begin the year as the Cubs' closer, though new addition Hector Neris gives manager Craig Counsell a possible alternative for the late innings, Jordan Bastian of MLB.com reports.