"Gul has been advised two weeks' rest after he damaged cartilage in the rib and we would officially request for a replacement," Salahuddin told AFP.
The 24-year-old limped off the field during Pakistan's six-wicket defeat against India here on Thursday.
Pakistan will have to officially request to the organisers of the Asia Cup for a replacement from outside the 15-member squad announced for the event.
Paceman Abdur Rauf, who was included in the 20-man initial squad but was not picked in the final 15-man team, is the likely replacement.
Pakistan and India qualified for the Super League stages of the event along with titleholders Sri Lanka and Bangladesh.
India take on Bangladesh in the first match of the Super League on Saturday. Pakistan play Sri Lanka on Sunday.
The top two teams qualify for the July 6 final, to be played in Karachi.