Cozart, 29, was off to the strongest start of his career and on pace for personal bests, with a .258 batting average, a .310 on-base percentage and a .459 slugging percentage in 53 games. He had at least 500 at-bats for the Reds in each of the past three seasons and never posted an on-base percentage higher than .288.
"[Cozart] has a significant role -- not just as great defensive player and off to a great start offensively -- but he's just one of those fabric-type players," said manager Bryan Price on Thursday afternoon. "He's a guy that's blue collar, goes unnoticed at times unless you're around him every day like we are, because he's just such a solid guy. He's such a tremendous person, on top of being an outstanding player."
The Reds selected Cozart in the second round of the 2007 MLB Draft, and he's played 498 games at shortstop for Cincinnati over the last five seasons. Cozart started 52 games at shortstop this year, and he finished 50 of those contests, making just three errors in 214 chances.
Eugenio Suarez, 23, will take Cozart's place at shortstop for the time being after spending the season with Triple-A Louisville. Suarez played shortstop for the Tigers last year, posting a .242 average and a .316 on-base percentage in 85 games.
Cozart's injury leaves Cincinnati with three regulars from its Opening-Day roster in Thursday's lineup. Only first baseman Joey Votto, third baseman Todd Frazier and right fielder Jay Bruce remain.
"Everyone plays under the same set of rules," Price said. "The depth of our organization will be tested. … No one feels sorry for you when you have injuries, and there are a lot of other teams dealing with the same thing we are.
"I think what we'll do is play our best baseball and see where things fall."
After they were injured earlier in the week, second baseman Brandon Phillips (minor left groin strain) and center fielder Billy Hamilton (left wrist) remain day to day, according to Price. Phillips has gone through treatment, Price said.
"I'm going to want to see [Phillips] out on the field taking ground balls, swinging the bat," Price said, "doing what he would on a normal pregame to be able to really assess if he can go out there and play at 100 percent without risk of creating a massive problem."
Hamilton is in a similar situation. On Wednesday, he hit off a tee and tossed a ball, but he won't be cleared until Price has seen him work out. Hamilton could be a "usable bench player" Thursday, Price noted, and could have gone Wednesday in an emergency.
"I would anticipate that if everything goes well [Thursday], that [Hamilton] would definitely play [Friday]," Price added.
• Price received more bad news after catcher Devin Mesoraco experienced soreness on Wednesday while playing the outfield for Triple-A Louisville. Mesoraco had two at-bats, going 0-for-2 with two strikeouts before he was pulled.
"He did not feel great yesterday, so we'll have to reassess his ability to go out there and play the outfield," Price said.
Thursday was already a scheduled off-day for Mesoraco because of a death in the family.
• The Reds released right-hander Jason Marquis on Thursday. Marquis, 36, had been designated for assignment on June 5 after he struggled early in the year.
In his last 18 innings, Marquis allowed 17 runs and 31 hits, and he posted a 6.46 ERA and 1.65 WHIP over 47 1/3 innings this season.