The Gills were given 38,000 tickets for the game with Shrewsbury and have less than 5,000 remaining, but after the Shrews applied to extend their original allocation to 21,000, segregation issues mean there are no more available for fans of the Kent club.
Chief executive Mark Jones told KentOnline: "Shrewsbury took an additional 5,000 tickets and because of the section of the stadium they took them in, it means that we cannot have more than 38,000 because of segregation and the agreements with the police.
"That will be our maximum and that includes the 3,000 Club Wembley tickets and another 400 corporate hospitality seats.
"I didn't know what to expect. I haven't experienced it here before but it shows the size of the club.
"We are allowing everybody to buy eight tickets per person now. Everybody can come now for the seats we have left."