The quarter-final second leg, which was declared "high risk" as is common for high profile Champions League games, comes after several European ties have been marred by violence.
"Nearly 1,800 officers will ensure that the match is held normally and that security is reinforced in and outside the stadium," Madrid city hall said in a statement.
"The police presence will also be reinforced in tourist areas of the capital," it added.
There were clashes last week in the heart of Madrid between Leicester City supporters and police before the English side's Champions League quarter-final at Atletico Madrid.
Fans claimed police used tear gas and rubber bullets against them as tensions boiled over in Spain and accused the authorities of being over zealous.
About 1,000 police officers had been deployed in and around Atletico Madrid Vicente Calderon stadium for Leicester's 1-0 first leg defeat.
Three explosions hit the Borussia Dortmund team bus last Tuesday, injuring the club's Spanish defender Marc Bartra, ahead of its Champions League quarter-final, first-leg, against Monaco in Dortmund.
Turkish fans clashed with security forces in Lyon ahead of Thursday's Europa League quarter-final at Parc OL and left a steward injured.
Some 4,200 Bayern Munich fans are expected to attend the match on Tuesday at Real Madrid's Santiago Bernabeu stadium, which seats around 79,000 fans.