Moore was making his second start of the season for the Rays and had held the Royals to just one run through 4⅓ innings before leaving the game with the injury.
Per Topkin, the Rays said "there's no reason to believe it's serious," and Moore will undergo an MRI on Tuesday morning before the Rays know anything more.
The injury to Moore comes at a time when Tampa Bay's rotation depth has already been stretched thin thanks to Jeremy Hellickson's elbow injury. Hellickson, who underwent arthroscopic surgery on his right elbow in February, is expected to be out until late May as a result.
Now Moore has come down with an elbow injury of his own, and although the Rays stated the injury isn't believed to be serious, elbow soreness can often lead to extended stints on the DL for pitchers. If Moore does miss any time, either Nate Karns, Erik Bedard, or Enny Romero could be in line to fill in for the left-handed Moore.
Initially debuting for the Rays in 2011, Moore has been a solid but inconsistent starter for Tampa Bay the past couple of seasons. The 24-year-old pitched 150.1 innings for the Rays in 2013, posting a 3.29 ERA, while striking out 143 batters and walking 76. This came a year after Moore's rookie campaign in which the 6-foot-3 southpaw finished with a 3.81 ERA and 175 strikeouts over 177.1 innings in 2012.
The Rays placed Moore on the DL with a sore left elbow last July as well, and he spent just over a month on the shelf before returning in September. So there is some precedent for Moore to experience elbow soreness, and the Rays will no doubt proceed cautiously with the left-hander.
If Moore's injury is serious, it could have a huge impact on the AL East. Injuries aside, Tampa Bay's pitching depth isn't as solid as in years past, and with the division race expected to be tight, the Rays need all the pitching they can get.
Perhaps Moore will be fine, but before Tampa Bay receives the results from tomorrow's MRI, the Rays can't be too certain about the state of their starting pitching.