Mick, the son of seven-time world Formula One champion Michael Schumacher, had an early exit in a Mercedes event in Stuttgart on Saturday where he raced against Rosberg, last season's runner-up in the F1 world drivers' championship behind winner Lewis Hamilton.
In a head-to-head in Stuttgart, Schumacher Jnr finished nearly two seconds behind Rosberg, who went on to finish fourth overall in the day's competition while Hamilton was third, in front of 40 000 spectators.
Rosberg, whose father Keke was the 1982 world champion, knows the pressure Mick is under to live up the family name after the teenager's debut season in Formula Four brought mixed results despite intense media interest.
Schumacher Jnr did not remove his helmet in front of television cameras in Stuttgart and gave just one interview, describing the event as “super fun and an honour to be here”, as reporters clamoured to speak to him.
WAY TOO MUCH HYPE
“Mick had it worse than I did. It's an incredible amount of hype,” said Mercedes driver Rosberg.
“I never had it like that and it's a pity as it must certainly take some of the fun of the sport away from him, but it's something he has to accept and live with.
“I always look to see how he's driving and I hope he can enjoy the racing despite all the hype.”
Rosberg's Mercedes team-mate and world champion Hamilton said Mick only needed to look at his father's career to get some inspiration.
“He certainly doesn't need any advice from me, he just has to look at what his father has done, because he is the greatest legend in our sport,” said Hamilton.
Michael Schumacher, 46, is recovering at the family home in Switzerland after being left with a serious head injury following a skiing accident nearly two years ago.
He retired from Formula One in 2012 having won the last of his seven world titles in 2004.
Original source: Why Rosberg worries about Shumi Jr