"Whether or not he has to have surgery will probably be the telltale," Melvin said. "Right now, we're still trying to figure out how severe it is in there and how far the tendon is off the bone. We will decide if surgery is the way to go or if it's not the way to go. We're still trying to wait on that one."
Byrnes has not been seen in the D-backs' clubhouse since the injury. He's hitting just .209 and was 4-for-8 on stolen-base attempts on the season, but the 32-year-old has been battling sore hamstrings since Spring Training.
"It becomes a decision on his part too, and whether or not he wants to do the surgery based on the opinions he gets after listening to all the proper personnel," Melvin said. "There will be a lot of eyes on this one."
The D-backs also learned catcher Chris Snyder will not need surgery to repair a fractured left testicle that he suffered on Monday night when a foul ball hit him.
Melvin said on Tuesday that Snyder was going to have surgery on Wednesday, but that changed after further medical review.
The timetable for Snyder's return is still the same and he is expected to be activated following the All-Star break.
As part of Melvin's seemingly endless injury update, Mark Reynolds was out of the lineup on Wednesday night after he took two hard shots off his left wrist the previous night while playing third base.
Reynolds had an MRI on his wrist, which showed no fracture. Melvin said he should be back in the lineup on Thursday. Reynolds said he begged Melvin to keep him in the lineup, but it wasn't enough.
Melvin said pitcher Micah Owings, who missed his start Wednesday night after injuring his gluteus muscle, will likely make his next start on Tuesday in Washington, but will be unable to fill pinch-hitting duties, adding that pitcher Dan Haren will probably get a few at-bats.
Relief pitcher Juan Cruz, who had rib inflammation, was "considerably better" and threw off the mound on Wednesday, and should be available for Wednesday night's game.
The D-backs may call up a position player on Thursday. They called up relief pitcher Connor Robertson from Triple-A Tucson to take Byrnes' spot, but currently have 13 pitchers on the 25-man roster, meaning the bench is limited to four players.
"Everybody has to go through a rash of injuries at some point during the season. It's just stuff we have to deal with right now," Melvin said.