In his first full professional season, Gilmartin has made 20 starts at Double-A Mississippi. In 119 1/3 innings, he has struck out 86 and walked 26. Gilmartin was also named to the Southern League All-Star team but did not pitch in the game.
Braves manager Fredi Gonzalez said he was excited to see how Gilmartin responded to the promotion.
"He's a guy that has pitched pretty good in Double-A," Gonzalez said. "And why not? Put him out there in Triple-A and see what he can do."
Ranked this season by MLB.com as the Braves' No. 5 prospect, Gilmartin was the 28th overall pick in last year's Draft after an All-American junior season at Florida State.
The date of Gilmartin's Triple-A debut has not yet been announced. He last pitched Tuesday, putting him in line for a start Sunday at Charlotte.