Ratliff was placed on the physically unable to perform list Sunday morning. The four-time Pro Bowler was able to finish the conditioning test on Saturday, but was hurt in the middle of the run that led the team to placing him on PUP.
"We'll evaluate [the MRI] and make our best decision with him," Cowboys coach Jason Garrett said.
Ratliff missed most of training camp last year because of plantar fasciitis and missed 10 games with ankle and eventual sports hernia surgery last season.
In their move to the 4-3 defense, the Cowboys need Ratliff to play a big role. However, the 31-year-old has had his sack totals decrease in each of the last five seasons.
"He's working through some things and we'll handle that," Cowboys executive vice president Stephen Jones said. "I'm not concerned."
Guard Mackenzy Bernadeau, who had offseason shoulder surgery and did not take part in the organized team activities and minicamp in the spring, also hurt his hamstring during the conditioning test and was placed on PUP. He will not have an MRI.
Bernadeau said he felt the strain on the 15th of 20 40-yard dashes he had to finish in six seconds each and felt it would be better not to aggravate it further by continuing to run.
It is the second straight year Bernadeau has not been able to practice at the start of camp because of injury. He missed most of training camp last year with knee and hip injuries but managed to start every game.
Starting defensive end Anthony Spencer missed the last hour of practice with a tweak of his left knee. Spencer hyperextended his left knee during offseason workouts and said the same knee is bothering him. He will have an MRI on the knee, a team source said.
"I'm day to day," Spencer said. "I ran the conditioning test [Saturday] and it's a little achy and I'm just being cautious."
Defensive end Tyrone Crawford suffered a season-ending torn Achilles in practice, a team source said.
The Cowboys also placed center Ryan Cook, guard Nate Livings (foot), guard Ronald Leary (calf), long-snapper L.P. Ladouceur (calf), tackle Demetress Bell and wide receiver Lavasier Tuinei on the active/non-football injury list.
Last year, running back Felix Jones, safety Brodney Pool and wide receiver Andre Holmes failed the conditioning test and were not cleared to practice until they passed it a few days later. Pool eventually was after beginning to practice.
A year ago, Garrett expressed disappointment in Jones, Pool and Holmes, but that was not necessarily the case on Sunday.
"Guys are coming off different situations here," Garrett said. "Felix had a couple of things he was coming off of, too, but bigger guys -- it's a hard test for the big guys and it's designed that way for a reason.
"They have to run 10 40s in six seconds [each]. ... It's not an easy test. Weight's always a factor with these guys. A couple of these guys are coming off injury and that's a factor."
Information from ESPNDallas.com's Calvin Watkins contributed to this report.