The man has been identified as a paramedic with the Harris County Emergency Corps, or HCEC.
HCEC CEO Jeremy Hyde released a statement late Sunday night about the employee's injury.
"He was immediately taken to the hospital, evaluated and is currently in stable condition."
Play between the Astros and New York Yankees was briefly halted after the accident in the fifth inning, and manager AJ Hinch came on the field to console a shaken-up Brantley.
"It was heart wrenching. We didn't know who it was, it was in the dugout, home dugout, and we weren't sure who got hit," said fan Cindy Taylor.
Springer with his arm around Brantley as they walk out to the outfield. Trying to help his friend shake off the foul ball that hit someone in the #Astros dugout. Very scary moment in Game 2 #TakeItBack— Greg Bailey (@GregBailey13) October 14, 2019
Several Astros players were shown in the dugout looking distraught, as were Yankees players who had a view into Houston's dugout. Houston stars Carlos Correa and George Springer both could be seen putting their hands on their heads and then looking away seconds after the ball entered the dugout.
Play resumed after a couple of minutes and Brantley struck out but reached first on a wild pitch by Adam Ottavino.
The Astros extended the protective netting at Minute Maid Park to cover more of the seating area earlier this year, but there is no such protection for the dugouts. The move came after a 2-year-old girl suffered a skull fracture when she was struck by a foul ball during a May game in Houston.
The Associated Press contributed to this report.