Jaguars coach Gus Bradley said Pasztor, who started 12 games at right tackle last season, will be evaluated in a month. The second-year player from Virginia started three games at left guard as a rookie in 2012.
Pasztor was wearing a cast on his hand in the locker room on Friday morning and said he isn't sure how he hurt his hand during the Jaguars' 20-19 loss at Chicago on Thursday night.
"Honestly, I don't remember what happened," he said. "It was on the last series that I was in there for, where we scored a touchdown, but I don't remember the exact play where it happened.
"I remember my hand hurting but not when it actually started hurting."
Cameron Bradfield, who has started 12 games at left tackle and 13 at right tackle in his three-year career with the Jaguars, will replace Pasztor in the starting lineup.
Pasztor was one of three offensive linemen who were injured against the Bears.
Rookie Luke Bowanko, one of three players who took reps at center, is scheduled to have an MRI to evaluate the sprained left ankle he suffered against the Bears. How much time he'll miss is uncertain. He is competing with Mike Brewster and rookie Brandon Linder to become the starter at center.
Reserve tackle Josh Wells suffered a shoulder injury and will have an MRI.
In other Jaguars injury news:
• Bradley said receiver Cecil Shorts (hamstring) and linebacker Dekoda Watson (groin) are expected to practice in a limited capacity Sunday and should get a few reps in next Friday's preseason game at Detroit. Watson was placed on the PUP list before training camp began and will be activated sometime before Sunday. Shorts injured his hamstring on the first day of camp.
• Middle linebacker Paul Posluszny will return to the practice field Sunday, Bradley said. Posluszny (biceps contusion) did not make the trip to Chicago.