D-backs manager Bob Melvin said he expects Byrnes to be out much longer than just the 15 days. He is hoping Snyder will require just two weeks to recover and will return after the All-Star Game when the D-backs open a three-game series with the Dodgers.
To fill their spots, the D-backs recalled right-hander Connor Robertson and catcher Robby Hammock from Triple-A Tucson.
The D-backs called up Robertson to fill Byrnes' spot because the bullpen had been taxed in recent days. Robertson's stay in Phoenix might be cut short with the need of a position player looming. Hammock arrived from Tucson during Tuesday night's game and was available. Melvin said Hammock will probably start Thursday's day game.
"We're going a position player short today," Melvin said on Tuesday. "We're a little thin in the bullpen. ... [Robertson] brings us some length."
Reliever Juan Cruz, who underwent an MRI on Tuesday, was not available during Tuesday's game because of a rib inflammation in his left side. Melvin is hoping he will be available on Wednesday.
Closer Brandon Lyon and setup man Tony Pena had both thrown in three straight games before Tuesday night, and Chad Qualls pitched 1 1/3 innings on Monday night.
In Monday's game, Byrnes was given the green light to steal with none out in the second inning. Melvin said before the game that he wanted Byrnes to expand his game. Just a year removed from a 50-stolen-base season, Byrnes was mired in a 2-for-22 slump. He led off the inning with a double, then strained his left hamstring as he neared third base.
"Part of him being back was him being healthy," Melvin said. "When he comes back, he's healthy and he runs the bases. That's the first time he really had to tax it like that. He felt pretty good up until the last couple of steps when it went on him.
"There are degrees of healthy. Over the course of 162 games, no one is 100 percent healthy, but being that he did what we asked him to do in the rehab in the times he was getting down the line, and how he felt and the feedback we were getting from him, he was healthy enough to come back and play on an everyday basis."
Mike Ritter is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.