Babar was hit on the finger by a fast delivery and left the field after receiving medical treatment. The Pakistan Cricket Board later advised him not to continue the practice game as a precaution.
Although Babar has since returned to training with his teammates in Headingley, his availability for the opening Test will depend on medical clearance.
Pakistan fast bowler Mohammad Abbas said the final decision on Babar’s participation would be made by the PCB medical team on match day.
Pakistan and England will begin their three-match Test series in Leeds on August 19.