Celtic have been granted permission to have about 9,000 fans in for their Champions League opener.
Aberdeen were earlier told they would have 5,665 supporters into Pittodrie for their first European match.
Celtic had hoped for a larger crowd for Tuesday's second qualifying round tie against Danish side Midtjylland, which comes a day after Scotland moves to Level 0 coronavirus restrictions.
Current rules state outdoor events can be held in front of 500 fans but organisers can apply to have up to 2,000, which Celtic have secured for their friendly against Preston on Saturday.
Rules from Monday allow organisers to host 2,000 people as standard at outdoor events but applications can be made to local authorities to accommodate larger crowds.
Celtic were informed of the capacity restrictions following a meeting with the local safety advisory group, which is made up of representatives from Glasgow City Council, the emergency services and building regulators.
A club statement read: "Clearly, we have worked tirelessly in this area, we had pushed for many more fans to be given access and of course we are disappointed that more supporters will not be able to attend.
"However, we really look forward to welcoming our fans for the match on Tuesday, as we do on Saturday when we meet Preston North End.
"We can assure our supporters we will be doing all we can to work closely with the relevant authorities and welcome our fans back in even greater numbers in the coming weeks."
Aberdeen had initially hoped to have 8,200 fans in for their first few matches of the season but expressed confidence earlier this week that they would be allowed 5,665 under one-metre social-distancing rules, following talks with council officials.
Dons supporters will need to provide proof of a negative lateral flow test to gain entry to Thursday's Europa Conference League clash against BK Hacken.
Chairman Dave Cormack said: "This is a major step in the right direction and we're grateful to the local authority for working closely with us to get to this stage.
"Ideally, we wanted to be able to accommodate all our season ticket members. However, 5,665 represents 73 per cent of the 7,800 season tickets sold to date.
"Based on our previous percentages of season ticket members take-up (55 per cent to 60 per cent) and the fact that some have indicated that they are not ready to attend games just yet, we believe we'll be able to accommodate all who want to attend."
Scotland is due to move beyond Level 0 restrictions on August 9, if the Scottish Government decides the data on Covid infections, hospitalisations and deaths allow for further easing of restrictions.
