Luis Enrique named a 24-man squad for the tournament on Monday, with Real Madrid captain Sergio Ramos the headline omission.
Ramos' absence would ordinarily mean a prominent role for Martinez, although he was another notable absentee, with Pau Torres, Diego Llorente, Aymeric Laporte, Eric Garcia and Cesar Azpilicueta comprising Luis Enrique's central defensive options.
Speaking at a news conference after the squad announcement, Luis Enrique did not go into detail over Martinez not being selected, simply saying there would be a statement after his briefing.
The 30-year-old then posted an explanation on social media, saying that he felt it was time to put his own wellbeing first for the good of both the national team and himself.
"Take a step to the side to disconnect, recharge the batteries and quickly recover the strength that has always accompanied me."