Both clubs were given 20,000 in a 50/50 split with Celtic given assurances that Hibs would sell their full allotment, according to the Daily Record.
However the Capital club were only able to shift around 10,000 tickets with the spare briefs not being returned to the SPFL for Celtic to use, meaning there will be 10,000 empty seats at Hampden.
This will cost the Celtic, Rangers and Motherwell £62,500 in each.
A spokesperson for Celtic said: “Celtic Football Club is extremely disappointed to learn so many tickets will be unsold for such a prestigious and eagerly awaited match.
“Hibernian demanded an even split of tickets but as it stands have only sold half their allocation.
“It is totally unacceptable that we have thousands more season-ticket holders wishing to attend the match but they will now not be able to, whilst thousands of seats lie empty.
“This is not for the first time this has happened and we will be writing to the SPFL on a matter which needs to be addressed.”