Rahul will also lead the side with Shikhar Dhawan named vice-captain
Brawn worked with Mick's father Michael at Ferrari as the older Schumacher dominated Formula One.
Michael Schumacher, who turned 50 in early January, drove for Ferrari from 1996 to 2006, winning five of his seven world titles with the team.
Mick, who turns 20 later this month, won the European Formula 3 title last season and has joined Prema, a team allied with the Ferrari Drivers Academy, in Formula 2.
"I've known Mick since he was a little boy and it's been fascinating," said Brawn who is now F1's sports director told the press on Wednesday night in London. "I think there was a period when he wasn't sure, but he has now got the bit between his teeth and he is a very determined young man."
The younger Schumacher dominated F2 testing in Spain in late February.
"I think it is fascinating how his competitiveness kicked in during Formula 3 last year, and you've seen it again in Formula 2 in the first test," Brawn said. "People who know him, or spend more time with him than I do, say there has been impressive progress in his driving career in the last 12 months or so."
"But he is a very nice young man, and staying like that with the pressures and challenges that come, that will be one of the things that will be challenging for him," Brawn said.
"He's got a very balanced family and they have all known the experience from Michael, so they will know how to handle it if Mick is successful."
Michael Schumacher suffered a ski accident at the end of 2013 and his health remains a carefully-guarded secret.
"There are so many times when I see Mick and I see Michael in him, so it would be wonderful. But there is tremendous pressure on the lad, so I hope people can keep that in perspective and not hook unrealistic expectations on him."
The Formula 2 season begins on March 29 in Bahrain.
Rahul will also lead the side with Shikhar Dhawan named vice-captain
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