Moore was placed on the 15-day disabled list two days after leaving an April 7 start against the Kansas City Royals with discomfort in his pitching elbow.
The 24-year-old left-hander missed over a month of the 2013 season with discomfort in the elbow but returned for the postseason.
"I would say it's quite a bit different in how it feels, in how it dangles, with regards to soreness," Moore said after being placed on the disabled list. "The discomfort is similar. The severity has jumped from what I was feeling. It's frustrating."
Moore was an All-Star last season, went he went 17-4 with a 3.29 ERA. He posted a 2.70 ERA in his first two starts this season.
The Rays have been plagued by injuries to their rotation. Alex Cobb, who posted a 1.89 ERA in his first three starts, was placed on the disabled list Sunday due to an oblique strain.
Tampa Bay also has been without right-hander Jeremy Hellickson, who underwent offseason elbow surgery and is not expected to return until June.
Several pitchers have been diagnosed with torn elbow ligaments, requiring Tommy John surgery, since the start of spring training, including Braves right-handers Kris Medlen, Brandon Beachy and Cory Gearrin; Diamondbacks ace Patrick Corbin; Athletics starter Jarrod Parker; Mets closer Bobby Parnell; Royals setup man Luke Hochevar; Tigers reliever Bruce Rondon; and Pirates top prospect Jameson Taillon.