Police raided six properties in the Madrid region and seized a gun, ammunition, manuals to cracking safes, laser devices and oxy-fuel cylinders used to cut metal, Spain's National Police said in a statement on Tuesday.
The three people were “directly connected” to the robbery and were part of a group that burgled homes across Spain, the statement said. Five other members of the gang were also arrested for a further 15 robberies.
The five paintings by Francis Bacon were stolen from the Madrid home of an art collector in June, 2015, who had reportedly been a close friend of the artist.
They were valued at around €25 million, ($26.88 million).
The thieves, who left no trace of their handiwork, had tracked the owner's movements to ensure he did not return to his apartment to catch them red-handed.
Irish-born Bacon died in Madrid in 1992 aged 82 and his expressionist-surrealist works, which are often raw and emotional, remain hugely sought after.
Bacon's death only enhanced his reputation and the 2013 sale of his 1969 work "Three Studies of Lucien Freud" fetched $142,405,000 at auction, a world record at the time.
Art market information leader Artprice lists Bacon as one of 10 frontline modern artists alongside the likes of Picasso and Andy Warhol Warhol whose works comprise 18 percent of global sales.