The 35-year-old midfielder said it was time to make way for the next generation after the team lost all three group matches at the tournament in Poland and Ukraine.
"I don't want to retire," Van Bommel said. "Maybe there will a moment that the coach needs me in the future and then I will be available but for now it is time for talented young players."
Van Bommel made his Netherlands debut in 2000 and won 79 caps, playing in two World Cups and one European Championship.
After helping the team reach the last 16 at the 2006 World Cup the midfielder announced that he would not be available for the national side as long Marco van Basten was coach.
But after Van Basten stepped down following Euro 2008, Van Bommel returned under new coach Bert van Marwijk, who is also his father-in-law, and he played a key role in helping the Dutch reach the 2010 World Cup final.
Van Bommel has joined PSV Eindhoven for next season after a seven-year stint abroad playing for Barcelona, Bayern Munich and AC Milan.