At least five people were hit including Mr Scalise, the House Majority Whip, when a gunman fired more than 50 shots with a rifle at Eugene Simpson Stadium Park in Alexandria, Virginia.
An aide to Roger Williams, congressman for Austin, Texas, was injured as the group practiced at around 7am local time.
The gunman has died fter he was shot by police.
President Donald Trump said: “The assailant has now died from his injuries.”
North Carolina Republican Mike Walker said the “gunman was there to kill as many Republican members as possible”.
Republican Mike Bishop, Michigan Representative, said: “As we were standing here this morning, a gunman walked up to the fence line and just began to shoot.
“I was standing at home plate and he was in the third base line.
“He had a rifle that was clearly meant for the job of taking people out, multiple casualties, and he had several rounds and magazines that he kept unloading and reloading.”
Mr Scalise was shot in the hip and is now undergoing surgery, but is in a stable condition.
Before the shooting, a man asked the Florida congressman Ron De Santis whether the politicians were Republicans or Democrats.
Both baseball sides were in training for a Republican v Democrat baseball games, due to take place tomorrow.
The game is set to raise funds for charity and is a political tradition.
The gunman is thought to be in his 40s or 50s and was armed with an AR-15 rifle.
President Donald Trump said that he and vice-president Mike Pence were “deeply saddened”.
He said: “We are deeply saddened by this tragedy.
“Our thoughts and prayers are with the members of Congress, their staffs, Capitol Police, first responders, and all others affected.”
The President later tweeted: “Rep. Steve Scalise of Louisiana, a true friend and patriot, was badly injured but will fully recover. Our thoughts and prayers are with him.”
Wednesday’s incident was the first shooting of a member of the U.S. Congress since January 2011, when Democratic Representative Gabby Giffords was seriously wounded in an assassination attempt at a gathering of her constituents in Tucson, Arizona.
Mr Scalise has been a strong opponent of gun control measures and has co-sponsored legislation to weaken gun control laws in the District of Colombia.
Witness, David Miller, said: “There was absolutely no shelter. They were in the middle of the ball park.
“They can’t run. If they get up they are a target.”