Capitol Police officers are being widely praised for helping to stop the attack.
"Many lives would have been lost if not for the heroic actions of the two Capitol Police officers, who took down the gunman despite sustaining gunshot wounds during a very, very brutal assault," President Trump said shortly before noon.
The shooting occurred around 7 a.m. ET in the Del Ray area of Alexandria, just south of Washington, D.C., about 8 miles from Capitol Hill. A helicopter arrived to medevac at least one victim.
The FBI has taken over the investigation because the attack involved violence against a federal official.
The FBI is "exploring all angles" in the case, Slater said, responding to a question about whether the attack was an act of terrorism.
Federal investigators are conducting emergency traces on the two firearms, an ATF spokesman tells NPR's Carrie Johnson.
In the wake of the shooting, the House of Representatives canceled legislative business for the day, and security was increased around the White House. A public event that had been scheduled by Trump at the Labor Department on Wednesday afternoon was canceled.
Scalise was shot in the hip and underwent surgery at MedStar Washington Hospital Center. "Prior to entering surgery, the Whip was in good spirits and spoke to his wife by phone," Scalise's office said in a statement. "He is grateful for the brave actions of U.S. Capitol Police, first responders, and colleagues."
The hospital said Wednesday afternoon that Scalise was in critical condition.
Trump said in a tweet that Scalise "was badly injured but will fully recover," adding, "Our thoughts and prayers are with him."
The shooter opened fire at a baseball field at Eugene Simpson Stadium Park, across the parking lot from Alexandria's YMCA. Gunshots hit the YMCA's windows, and the building was shut down and the block cordoned off, NPR's Tom Bowman reported from the scene.
After receiving a call of shots fired at 7:09 a.m., officers arrived within three minutes, Alexandria Police Chief Mike Brown said. By 7:14 a.m., the FBI says "the subject was engaged by law enforcement and shot." At least two officers fired at the gunman, Brown added.
Rep. Mo Brooks of Alabama, who was at the practice, told CNN that the gunman was holding what he described as a semi-automatic rifle in the area behind third base and that Scalise had been near second base. Brooks told CNN that he tried to help Scalise, saying, "We used my belt to help put a tourniquet around his leg."
Two Capitol Police officers showed "incredible bravery," Brooks said, describing how they used their pistols to engage in a gun battle with a man armed with a rifle, from a distance of 90 to 120 feet.
Rep. Steve Pearce of New Mexico, who was at the practice but unharmed, tweeted prayers for the victims.