Those at the field were Republican; the Democrats practice separately.
Sanders said he was "sickened by the despicable act".
Both sides were training, on separate fields, for a Republican v Democrat baseball game, scheduled for today.
The game is a long-standing political tradition, to raise money for charity. Both sides had been training for weeks.
At least five people were hit when more than 50 shots were fired by Hodgkinson.
Hodgkinson, believed to be using a rifle, opened fire behind the third base of the baseball field, on East Monroe St in Del Ray, Alexandria.
He then moved forwards and was met by return fire from Capitol police, assigned to protect Scalise, as a senior politician.
Many of those on the field have said that if Scalise was not there, and as a result the politicians were not protected, far more people could have been injured.
An aide to Roger Williams, congressman for Austin, Texas, was shot, the congressman's office confirmed.
Two Capitol Hill police officers are also thought to be hurt.
Their condition is said to be stable.
President Donald Trump said he and Vice President Mike Pence were "deeply saddened" and "monitoring developments".
"We are deeply saddened by this tragedy," he said.
"Our thoughts and prayers are with the members of Congress, their staffs, Capitol police, first responders, and all others affected."
He then gave an address from the White House, praising the police and confirming the death of Hodgkinson.
"Everyone on that field is a public servant," said Trump.
"Our brave police, congressional aides who work so tirelessly, and congressional members representing the people.
"We may have our differences, but everyone who serves is here because we love our country.
"We can all agree we are strongest when we are unified and we work together for the common good.
"Please take a moment today to remember those who serve for the common good."
Earlier he tweeted his support, confirming that Scalise was in a stable condition.
Gabrielle Giffords, the Arizona congresswoman who was shot in the head while campaigning in Tuscon on January 8, 2011, tweeted her condolences.
Local police tweeted at 7.30am local time (12.30GMT) that they were investigating a multiple shooting and a suspect was believed to be in custody.
This article originally appeared on the Daily Telegraph.