South Carolina congressman Jeff Duncan said the suspect had asked him whether Republicans or Democrats were practising before shots rang out.
Mr Brooks said the gunman was armed with a rifle and was "blasting away" from behind the dugout, using it for protection. The congressman, who said he took refuge behind a batting cage, described the attacker as a middle-aged white male, "a little on the chubby side"
The last member of Congress to be targeted by a gunman was Democrat Gabrielle Giffords, who was shot in the head as she met constituents in Tucson, Arizona, in January 2011. She survived, but six others died in that incident.
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