The Scottish champions had hoped to receive permission for around six times that amount based on the calculations that allowed Hampden Park to host 12,000 fans during the European Championship.
However, Gers have been told they can fill just four per cent of their stadium capacity following discussions with the Scottish Government and Glasgow City Council.
Rangers fans have not been able to watch their side in action since 47,494 took in a 3-1 defeat to Bayer Leverkusen in the Europa League on March 12 last year.
A club statement read: "Following lengthy discussions with the Scottish Government and local authorities, Rangers have been granted permission to host 2000 supporters at Saturday’s friendly match with Arsenal.
"Season ticket holders who have access to all games at Ibrox will be given priority with the balance being balloted among season ticket holders who are MyGers members and have enrolled in the home friendly scheme.
"Those who are successful in the ballot will receive an email outlining arrangements for Saturday’s match.
"Rangers are disappointed at the small number of supporters being granted access given the precedent which was set at the Euro 2020 matches at Hampden Park as well as at other sporting events in Scotland, and the time it has taken to have the number of supporters confirmed by the Scottish Government.
"Discussions between the club and the relevant authorities continue for the Brighton and Real Madrid games on 24 and 25 July.”