The 22-year-old scored 19 goals this season before injuring his back against Wolves last month, with Ole Gunnar Solskjaer fearing he could miss the rest of the season.
"He should take a proper rest, like literally sit down on his sofa, rest for the next couple of weeks and let it heal," van Persie said.
"You have to look at it in two stages. The first bit, six to eight weeks, is doing nothing and then the next eight weeks is to get back to fitness again.
"You really have to see it in two stages and for him, he has to think about his future because he is the future of Manchester United."