At 21, Rashford has already become an established member of the first-team at club level and is also considered one of Gareth Southgate's most important players on the international stage.
Ole Gunnar Solskjaer has helped to bring out Rashford's best over recent weeks, with the forward starring for United in a central striking berth.
More is expected in the seasons to come, but Allardyce believes the demands set to be placed on him may lead to early retirement.
“Because of the demands, physically and mentally, the fatigue that he will suffer. He will have three weeks a year off. That’s it.
“He’ll play all over the world because there’s no pre-season anymore, they go straight away across to these tournaments.
“He’ll play for his country in the summer and he’ll get barely three weeks off.
“I think when you look at the wear and tear… by 25, he will have niggles. Even if he doesn’t get any major injuries, the knees and the ankles, the hips, the back will be a little bit of a problem as he goes on.
“They won’t stop him playing but I think later on in life it will bring his career to an end quicker than before.
“But if you look at the Premier League now, I think there’s less players over 30 playing now than ever.”
Rashford started and scored on what was his 150th appearance for United in their 2-1 win over Brighton on Saturday.
He will be hoping to again be selected for the FA Cup clash with Arsenal on Friday, although Romelu Lukaku will also be pushing for a recall having started just once since the Norwegian's appointment as interim boss.