Matsuda, who won 40 caps for Japan and represented his country at the 2002 World Cup, had been put on an artificial respirator after arriving at hospital unconscious on Tuesday.
Hiroshi Otsuki, the president of his JFL (third division) side Matsumoto Yamaga, told Japanese media the club had been informed Matsuda had lost his fight by the player's family.
"It's terrible to see someone die at such a young age," former Japan coach Philippe Troussier, who gave Matsuda his international debut, told Reuters.
"It's a big shock. He was a great guy and I felt a close bond to him. My thoughts go to his family.
"He was a reliable and strong player and key for Japan's World Cup side in 2002," added the Frenchman, who led the Blue Samurai to the last 16 as co-hosts.
"It's bad news for Japanese football. We'd all hoped of course he would pull through. To see someone taken away doing something they love, so suddenly, at 34 is tragic. It's awful news."
Medical personnel had rushed to Matsuda's aid early on Tuesday after he collapsed with suspected heatstroke. Yamaga later said the player had gone into cardio-respiratory arrest.
Record temperatures across Japan have caused a rise in heatstroke cases with 43 deaths in the two months through the end of July, according to Kyodo news agency.
Matsuda made 385 appearances for Yokohama F-Marinos, helping them win back-to-back J.League titles in 2003 and 2004.
