The track first appeared online in rough demo form in November, under the name 'Give Me All Your Love'.
Reuters reports that the 31-year-old man, whose identity was only referred to by his initials J.M.R., was arrested in Zargoza, Spain on Wednesday and was released after being charged.
Lawyers for Madonna had traced the leak to the suspect and police apparently found the recordings in his belongings. He is said to be "a big Madonna fan".
Madonna previously expressed anger over the leak, claiming that her true fans would never do something like that if they truly cared about her.
The final version of 'Gimme All Your Luvin' includes features from Nicki Minaj and MIA.
Madonna recently signed a three-record deal with Jimmy Iovine's Interscope Records.
Watch the video for Madonna's 'Give It 2 Me' below: