The team boss admitted that he does not like giving team orders, but insisted that it was necessary in this case.
Brawn revealed that there is no number one, and Hamilton, who joined from McLaren this season, only wanted parity during his negotiations.
"Of course Lewis wants to race," Brawn told Sky Sports. "In the contractual negotiations we had with Lewis, never was the issue of who is number one or number two brought up from his side.
"All he wants is parity - the same equipment, the same opportunity and that is great that he has that confidence and that approach, that he doesn't want favouritism."
The next race meeting in the Formula 1 calendar is in China on April 14.