The shooter was killed by police.
It happened during a Republican practice for the Annual Congressional Baseball Game held for charity.
Scalise, 51, the No. 3 House Republican leader, was first elected in 2008. In a statement at the White House after the shooting, President Trump broke the news Hodgkinson "has now died from his injuries".
Hodgkinson has been identified as the suspect in the shooting of House Majority Whip Steve Scalise and several other people in Virginia Wednesday morning, according to a government official. He was tended to by fellow lawmakers including Brad Wenstrup, an OH congressman who is a physician, before being transported to a hospital.
Five people were transported medically from the scene in Alexandria, city Police Chief Michael Brown told reporters.
After tending to Scalise, Brooks said, "Shortly thereafter the police showed up, and a helicopter landed in center field and took away whomever the folks decided was the most wounded, most critical".
The two lawmakers said they felt this was an important moment to try to improve relationships between members of Congress.
"Virginia public safety officials are coordinating with local responders and we will continue to monitor this situation and make every resource available".
Hodgkinson's Facebook page indicated that, until recently, he ran a home-inspection business out of his home in Belleville, in the southwestern corner of the state, across the Mississippi River from St. Louis.
Federal Bureau of Investigation special agent in charge Tim Slater said it was "too early to say" whether it was an act of terrorism, or whether Mr Scalise was targeted.
Support for U.S. House Majority Whip Steve Scalise and other victims of a shooting at a Republican baseball practice poured across social media Wednesday morning from Kansas lawmakers and others.
There will be plenty of security at the charity baseball game, which is to be played as scheduled Thursday.
Two lawmakers who were at the scene, Representatives Ron DeSantis and Jeff Duncan, indicated there might have been a political motive in the attack. "He knew who we were".
Roughly 15-25 people were at the practice, including Sens. "The field was basically a killing field if you were to run out there while the shooter was still shooting".
Representative Mo Brooks told CNN that during batting practice he heard a "bam" and then a quick succession of shots and saw the gunman shooting through the holes in a chain link fence. "Those aren't good odds", Brooks said. This is the second colleague of mine that's been shot since I've been in Congress, but our job is to go out and talk to our constituents.
The wounded also included two Capitol Police officers, a congressional aide, and a lobbyist who formerly worked in Congress, the Washington Post reports.
Capitol Police do occasionally assign an officer to attend baseball practices on a case-by-case basis.
The ensuing chaos drew about 100 police officers from different departments within minutes, according to witnesses, and helicopters swooped in to airlift the injured from the baseball field in suburban Alexandria, Va., outside Washington. "It's not a secret we are practising".
Murphy has been a vocal proponent for stricter gun control laws.