"We ask, your excellency, to not give Israel the honor to host the next UEFA Under-21 Championship," Rajoub said, in a letter seen by The Associated Press on Thursday. "We are deeply concerned about the situation of our footballers."
UEFA declined official comment.
Israel is set to stage the eight-nation tournament across four venues from June 5 to 18 next year.
The UEFA executive committee voted for Israel in January 2011 over competing bids from Bulgaria, the Czech Republic, England and Wales.
Rajoub is pressuring Platini to intervene on Palestine's behalf as player Mahmoud sarsak approaches a fourth month on a hunger strike.
Israel has jailed Sarsak for three years as an "illegal combatant" after he was stopped at a Gaza Strip checkpoint while traveling to an international match, Rajoub said.
"For athletes in Palestine, there is no real freedom of movement, and the risks of being detained or even killed are always looming before their eyes," he wrote.
Rajoub's letter named two other players, Omar Rweis and Mohammad Nimer, who are also being held without trial.
FIFA President Sepp Blatter and the global network of players' unions, FIFPro, support Sarsak's case.