He was in a critical condition Wednesday night and doctors said he would need several more operations.
Williams hurt his ankle diving into the dugout but his concern turned to one of his staffers, Zach Barth who had been shot.
One Capitol Hill police officer suffered a gunshot wound. Two congressman said they had sustained minor injuries while trying to take cover.
The gunman, identified by a senior U.S. official as James Hodgkinson from the St. Louis suburb of Belleville, Illinois, died of his injuries. Hodgkinson, who is from IL, is dead.
Hodgkinson's Facebook page is largely political, his profile picture is a caricature of Bernie Sanders as Uncle Sam, while his feed is filled with anti-Trump sentiments such as "Trump is guilty and should go to prison for treason".
Rep. Mo Brooks, an Alabama Republican, said his colleague "crawled into the outfield, leaving a trail of blood". Bernard Sanders' left-wing presidential campaign a year ago, had meant to harm Republicans.
"Let me be as clear as I can be".
Mr Sanders said he condemned the violence "in the strongest possible terms".
The popular annual face-off, which raises money for charity, is scheduled for Thursday evening at Nationals Park across the Potomac River in Washington, and will take place as planned.
He is an avid baseball fan and has played on the congressional baseball team since he entered Congress in 2008.
Capitol Police officers who were in Scalise's security detail wounded the shooter, who was taken into custody.
U.S. Sen. Rand Paul (R-Ky.), who was in the batting cage when he said the first of the 50 to 60 shots hit, told MSNBC, "Everybody probably would have died" if the Capitol Police officers weren't there protecting a member of leadership.
"There's just no way that I would have guessed that this guy would be shooting at law enforcement and a congressman", said Brennwald, an attorney.
When the shooting started, Rep. Trent Kelly of MS, playing on the third base side of the field, was facing the gunman and was the first target, lawmakers said. Some things that get reported by the media will later turn out to be wrong.
"Nobody would have survived without the Capitol Hill police".
According to a source, when Democratic members of Congress practicing at a different ballfield miles away heard of shooting, they immediately stopped and said a prayer together, CBS News senior investigative producer Pat Milton reports. "My colleagues were targeted today by somebody who wanted to kill them".
Barton had arrived at the US Capitol still wearing his red baseball uniform.
On the Senate side, Republican Majority Leader Mitch McConnell and Minority Leader Chuck Schumer skipped their usual partisan opening speeches, and instead admonished the horrific attack and thanked the Capitol Police officers who saved lives on the field.