Martinez has established himself as a highly-regarded talent and has received international recognition by Argentina at Under-20 level although he is yet to make his senior debut.
The 21-year-old joined the Gunners' Academy in 2010 and was quickly handed a place in Arsene Wenger's first-team squad at the Emirates Stadium.
He completed a loan spell with League Two side Oxford towards the end of the 2011/12 season, making just a solitary start.
Martinez went on to enjoy two Capital One Cup outings for Arsenal last term, appearing in a 6-1 rout of Coventry and the memorable 7-5 victory over Reading at the Madejski Stadium.
Martinez will compete with Chris Kirkland for the Owls' number one jersey ahead of Saturday's trip to Bolton in the Sky Bet Championship.
Dave Jones' struggling Wednesday side are one of only four teams in England's top four divisions still to record a league victory this campaign.