The Rays said Jennings, out since April 26, had tissue inflammation. Dr. Steven Singleton operated Wednesday in Vail, Colorado.
Tampa Bay manager Kevin Cash said there is no timetable for Jennings' return.
Rays left-hander Matt Moore, coming back from elbow ligament replacement surgery last year, expects to make his third minor league rehab start Monday for Class A Charlotte. He could be back by the end of the month.
Moore threw four scoreless innings Tuesday night for Charlotte against Dunedin and said Wednesday he "took a good step forward."
Tampa Bay third baseman Evan Longoria was set to start Wednesday night's game against the Los Angeles Angels after being out of the lineup the previous three games due to a sore left wrist.
The Rays recalled right-hander Preston Guilmet from Triple-A Durham to take the spot of left-hander Enny Romero, who was optioned to the International League after Tuesday night's 8-2 loss to the Angels.
Reliever Kirby Yates (strained right pectoral) was activated from the 15-day disabled list and optioned to Durham.