"We're still in the process of gathering information," said Red Sox manager John Farrell after Friday's 4-2 loss to the Indians.
Prior to the game, Farrell was optimistic that the injury won't require surgery.
"I would be surprised given what we know right now," said Farrell.
To replace Smith on the roster, the Red Sox recalled right-hander Noe Ramirez from Triple-A Pawtucket.
Smith made his return on May 3 and pitched a scoreless inning in Chicago. His elbow started to worsen after a 27-pitch inning against Oakland on May 9. Smith pitched just once after that.
"I threw against Oakland and had an extensive outing and a number of warmup pitches to go into that game, and since then, there's been small symptoms of what it was back in Spring Training," Smith said. "Right now, we're waiting on the results."
It was on March 21 that Smith was diagnosed with a flexor mass strain in his elbow.
"It's the same area," said Farrell. "He felt it probably more on the slider than on the fastball. While some of the throwing program was still intense over the last series in Kansas City, he was expressing enough discomfort that I wasn't going to put him in the game with that kind of feel."
Ramirez, 26, will begin his fourth Major League stint with the Red Sox this season. The right-hander was most recently recalled as the club's 26th man for Thursday's doubleheader in Kansas City, but he did not appear in either game. After making his first career Opening Day roster with Boston in 2016, Ramirez has appeared in nine games for the club, posting no record with a 5.79 ERA and 10 strikeouts.
Ian Browne has covered the Red Sox for MLB.com since 2002. Follow him on Twitter @IanMBrowne and Facebook. This story was not subject to the approval of Major League Baseball or its clubs.