Pittsburgh manager John Russell said the ball hit Meek on the top part of his hand near his fingers.
"No fracture, which is good," Russell said. "Really lucky."
Meek was struck in the eighth inning and walked off with trainers gingerly holding his right arm.
Meek was facing his fourth batter when Braun hit a 1-2 pitch that struck Meek, deflected off his chest and rolled to third for a single. Meek was knocked backward by the impact.