The application process began on February 28. The allocation of tickets will now be decided by lottery. Each successful candidate will be entitled to a maximum of two tickets, UEFA said on its website.
The UEFA Champions League final takes place at the Luzhniki Stadium in Moscow on Wednesday May 21. Kick off is at 10:45 p.m. local time (07:45 GMT).
While there are no Russian clubs left in Europe's most prestigious club competition, there is a good chance that at least one English team could make the final as Chelsea, Manchester United, Arsenal and Liverpool have all made the last eight.
Both British and Russian media have reported that Roman Abramovich has booked up hotels, nightclubs and restaurants across the Russian capital in anticipation of a big night out should Chelsea lift the trophy. The club have never made the final of the Champions League, losing three times at the semi-final stage, twice to Liverpool.
Roman Abramovich, who is also the governor of the Chukotka Autonomous Area in Russia's Far East, bought Chelsea in 2003. The side has won the English Premier League twice since then.
