A congressional aide said Scalise is undergoing surgery at George Washington University Hospital.
He praised the efforts of U.S. Capitol Police and other first responders.
The president expressed relief that Scalise, a Louisiana Republican, will recover from his wounds, and he offered thoughts and prayers to the lawmaker.
Sen. Rand Paul, R-Ky., told ABC News in a telephone interview that he was in the batting cage when he heard gunshots.
Michael L. Brown wouldn't identify them or give their conditions. He said the FBI has joined the investigation.
According to initial reports, Scalise appeared to have been shot in the hip.
"Nobody would have survived without the Capitol Hill police", Paul said on CNN.
The statement does not mention any of the victims by name.
Scalise is the first member of Congress to be shot since former Arizona Rep.
In a statement Wednesday, Williams said that at about 7 a.m. this morning, a gunman arrived at the practice and opened fire.
He said that one of the security detail had been shot in the chest and airlifted by helicopter.More news: Putin critic Alexei Navalny among hundreds jailed over anti-Kremlin protests
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Paul said there seemed to be a danger to stay or run, but he chose to run when, Capitol police started returning fire and gunman.
South Carolina Congressman Jeff Duncan says he believes he saw the shooter, but left before the incident began.
"All of a sudden we heard a very loud shot".
"[Scalise] was dragging his body away from second base to get away from the shooter", Brooks said of the moments following the attack, which he witnessed from a nearby deck.
The identity of the other staffers injured in the shooting remains unknown.
Sen. Jeff Flake, who was at the baseball practice, told reporters he called Scalise's wife to alert her of the situation.
On behalf of Jefferson Parish residents, who are so well represented by this tremendous leader, our thoughts and prayers are with him and those injured in the tragic incident in Virginia.
He said other people were also shot, including two police officers.
Capitol Police said officers who were part of Scalise's security detail returned fire and wounded the shooter, who was taken into custody, the AP reported.
President Donald Trump says he and the vice president are "deeply saddened" by news of a shooting "tragedy" at a congressional baseball game.