England international Rashford, who was injured for United's 1-0 defeat to Newcastle United last weekend, has not started any of the club's last six Premier League encounters.
Henry told Sky Sports' Monday Night Football that, with Jose Mourinho prepared to pick Alexis Sanchez, Anthony Martial and Romelu Lukaku ahead of the 20-year-old, Rashford must not suffer from a lack of momentum.
"One of the most important things for me is that you have to play," the Frenchman said. "You cannot be on the bench and missing games, missing learning about the game and stopping that momentum, and an example is Rashford.
"Michael Owen had the opportunity to back up what he did the year before because he played, and he played, and he played, and he played - and I can give you more examples. But Rashford at times could not capitalise on what he did from that year [after his debut], because sometimes he is playing on the right, [sometimes] on the left.
"Leave is a strong word. Obviously being from there, he wants to play for United. But he has to play and it is becoming even more difficult for him since Sanchez has arrived. I think at the end of the season, he is maybe going to have a thinking day of 'do I stay?'".
United's next game is against Huddersfield Town in the FA Cup on Saturday.