Despite Rashford breaking into the full England squad, national team manager Gareth Southgate has said he would like to have the 19-year-old at the youth tournament in Poland.
But faced with a growing injury list, Mourinho said he doesn't want to see Rashford playing at age-group level.
"I just feel that when a player reaches a certain level, it doesn't make a lot of sense to drop levels," he said. "It's like him going to play now in the (United) Under-23s to win, let's say, a derby against Man City. No. (Academy coach) Nicky Butt doesn't take him to play that game. He could, by age," added the United boss.
United lost striker Zlatan Ibrahimovic to a knee injury during Thursday's Europa League quarter-final win over Anderlecht but Mourinho said Rashford "cannot play every game".
French striker Anthony Martial, recently challenged to improve his approach by Mourinho, replaced Ibrahimovic for extra-time on Thursday and could now be given a bigger chance to stake his claim.
Mourinho used Jesse Lingard in attack with Rashford, to good effect, during Sunday's Premier League win over Chelsea at Old Trafford.
Wayne Rooney, who has been sidelined with various injury problems in recent weeks, could be ready to make a return for Sunday's visit to Burnley.
Read the full article on eurosport.co.uk: Mourinho says no sense in Rashford playing for England Under-21s