The bullet traveled across his pelvis, fracturing bones, injuring internal organs, and causing severe bleeding.
Investigators studying the attack at a suburban Virginia park said Hodgkinson had obtained his rifle and handgun from licensed firearms dealers.
"Both were purchased by the shooter from federal firearms licensees", the Capitol Police said in a statement. "We now have no evidence to suggest that the purchases were not lawful".
Vice President Mike Pence earlier on Thursday said he visited the hospital where Scalise was being treated.
When the members of the Republican team were announced at Nationals Park, mention of Scalise's name drew a standing ovation from the areas designated for Republican, Democrat and nonpartisan fans alike.
The shooting has raised questions about lawmakers' security, renewed the nation's contentious debate over guns and drawn new attention to the harsh rhetoric that reflects America's political polarization.
"But as you all know, tonight's game has taken on a much deeper level of meaning, beyond anything that we would have thought". Besides letting some of us relive our younger and more athletic days, it also gives us a rare opportunity to connect with our colleagues across party and state lines. We all salute them.
Even with lawmakers' determination for baseball bipartisanship, they say competitiveness remains.
Shannon Davis, who was on her way to work, said she received a frantic phone call from her husband.
Democrats defeated their Republican counterparts in the annual Congressional Baseball Game, but the biggest applause came for one who didn't play.