Rashford has burst onto the scene at Old Trafford in recent weeks after getting his chance amidst Louis van Gaal's injury woes.
A brace on his debut against FC Midtjylland in the Europa League was followed by another double on his Premier League debut against Arsenal as United defeated Arsene Wenger's title hopefuls 3-2.
Rashford's name has already been mentioned in some quarters with regards a potential call-up to Roy Hodgson's England squad.
But Shearer, who knows a thing or too about making a success of a career as a striker having scored a record 313 goals in 622 career games for club and country, has a stark warning for Rashford in his latest Coral column.
'Don't do a Macheda'
The pundit says the youngster needs only to look at the fate which befell former United prodigy Federico "Kiko" Macheda, now at Cardiff.
"We’ve seen it many times before at both at Manchester United and elsewhere with kids coming through early in their careers, Macheda is a prime example of that," Shearer said on Coral.
"He was meant to be the next big thing after he scored at a young age for the first team. Five or six clubs later, at the age of 24, he is now at Cardiff. Rashford should not go chasing the rewards."
Shearer went on to use himself as an example to Rashford as he recalled scoring a hat-trick on his debut for Southampton at the age of 17 - a year younger than Rashford is now.
'Learn from me'
"I then didn’t score for five or six games afterwards because people work you out and you have to work out how to adjust your game to overcome that," Shearer added.
"The lad has had a fantastic start though and it is great to see."
The tale of Macheda is a worrying one for any wannabe Old Trafford stars.
After just four goals in 19 games for the Red Devils, the Italian was loaned out to Sampdoria, Queens Park Rangers, VfB Stuttgart, Doncaster Rovers and Birmingham City before being released in 2014 when he signed for the Bluebirds on a free transfer.
He has hardly been a revelation in Wales either with just six goals in 21 games in his 18 months there.