Last season, the Argentine international, who came through the Gunners' academy in 2009, featured in the first team just five times and kept three clean sheets.
So far, the shot-stopper has played for Arsenal 50 times in his career, and he has had various loan spells at Wolverhampton Wanderers, Rotherham United, Sheffield Wednesday and Oxford United.
A statement on Arsenal's official website read: "Emi now heads to Spain to gain further first team experience. We'd like to wish him well for the year ahead."
Martinez joined the Gunners youth system from Independiente in 2010.