Rashford has been ruled out for at least six weeks after aggravating a back injury against Wolves last week after coming off the bench for a 16 minute cameo.
Van Persie suffered a similar injury when he was playing and was ruled out for four months.
The Dutchman has told Rashford to not force his comeback and let nature do its job of healing him.
“I had a similar injury, a stress fracture in my lower back," Van Persie told the Premier League.
“I was out with that for four months. You can't really do much, just rest and let it heal.
“But it is a difficult one because it always stays a little bit of a weakspot. Even now, it is not that I'm like in pain or something, but it's a sensitive area. So you have to be really careful with that."