Vettel, 32, disobeyed orders to let 21-year-old Leclerc pass him to lead Sunday’s Russian Grand Prix.
The German four-time world champion is fifth in the Formula 1 standings, 21 points behind the Monegasque in third.
“It’s a potentially explosive combination and needs careful handling,” said Brawn.
“Ferrari has made a lot of progress but it still has to deal with the balance between its drivers.”
Since the French Grand Prix in June, Leclerc has out-qualified Vettel nine times in a row, at an average advantage of more than 0.4 seconds a lap. He also has six poles and two wins this season to Vettel’s one.
Ferrari wanted to fashion a one-two finish in Sochi and achieve a fourth straight race win, but instead the one-two went to Mercedes, with LeWIS Hamilton taking the chequered flag followed by Finnish team-mate Valtteri Bottas.
The Briton now leads Bottas by 73 points at the top of the world title standings.
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Brawn was with Ferrari during their years of dominance when Michael Schumacher won five successive world titles between 2000 and 2004. Now he is backing current team principal Mattia Binotto to resolve any problems within the team.
“The honour and obligation falls to him [Binotto] to make sure that the mechanism that drives what can be a healthy rivalry runs smoothly,” he said.