Martino added he did not want the Barcelona forward, who will captain Argentina at the Centennial Copa America in the United States in June, to suffer burnout after a demanding season.
He can take three over-age players in his under-23 squad to the Rio Games but Messi, who helped Argentina win their second Olympic football title in Beijing in 2008, will not be one of them.
"Messi won't go to the Olympic Games because there is a lot of competition for the national team this year," Martino said with World Cup qualifiers also in mind.
"We have the Copa America, the Olympic Games and after that four rounds of the qualifiers," he told Radio La Red.
"The reality at Barcelona shows the season will be long. I want to win very much but not at any price, nor for throwing the players on to the pitch for them to die there."
Messi led Argentina to the 2014 World Cup final in Rio where they lost 1-0 to Germany after extra time.
The 16-team Copa America, to celebrate 100 years of the world’s oldest active international football tournament, will be played from June 3-26 with the 10-member nations of South America's CONMEBOL and six from rival region CONCACAF taking part.
Argentina, who also won Olympic gold at the 2004 Athens Games, failed to qualify for London 2012.
(Writing by Rex Gowar; Editing by Tony Jimenez)
