Edwards caught a 21-yard pass from Alex Smith on the 49ers' second play from scrimmage. He walked off the field and received treatment on the sideline before heading to the locker room.
Coach Jim Harbaugh had no update after the game.
San Francisco signed Edwards to a $3.5 million, one-year contract. The 49ers already had started the game short-handed with receiver Michael Crabtree inactive with a troublesome left foot injury.
Ted Ginn Jr. moved into the second receiver slot.
The 49ers lost to the Cowboys 27-24 in overtime.
Information from The Associated Press contributed to this report.