Leclerc, who will drive in his first race for the Italian team on Sunday, following a switch from Sauber at the end of last season. The 21-year-old has been tipped to give Vettel a run for his money at Ferrari in his first season.
He topped two days of pre-season testing in Barcelona, and finished just 0.010 seconds off his team-mate - who finished with the quickest time of the whole fortnight in Spain.
Asked if he thought Leclerc could out-perform Vettel in his first season at Ferrari, Brawn replied to Autosport: "I'd be surprised, if I'm honest, Sebastian is very good.
"If it unsettles him a little bit, I think that's the thing that the team will have to manage, not necessarily Charles beating him, but the fact that he could unsettle him."
However, even though Brawn doesn't believe the Monegasque driver can beat the German in 2019, he did single out the driver to be the young driver to watch for the upcoming season.
"I think he's the number one in that respect," Brawn continued on Leclerc. "He's had a very good first year, and he's now in a top team. Talking to some of the people I know at Ferrari, they've been very impressed with his approach and attitude. I think he's pretty special."