The occupants of the white van appeared to be OK, although at least one rear side window was was damaged. Clinton campaign chairman John Podesta was seen at the crash looking perplexed.
The carriage entrance is the area under the Senate steps that acts as a protected area to drop off senators and other VIPs. The scaffolding is part of a long-running renovation project at the Capitol.
Clinton and her team were heading to Virginia for a campaign rally.
Clinton was on the Hill meeting with the Democratic senators just days after primary opponent, Sen. Bernie Sanders, formally ended his bid and endorsed her. The gathering also comes amid poll news which shows the race tightening nationally and following a wave of negative news surrounding Clinton's use of a private email server when she was secretary of state.
Senate members in the meeting said Clinton discussed how difficult of a campaign this would be.
"There's no question she knows it's going to be tough," said Sen Richard Blumenthal of Connecticut. "One thing that impressed me about her energy and spirit is she knows it's going to be a rocky road."
New York Sen. Chuck Schumer, however, called the meeting a "love fest," and Sanders' appearance at the meeting helped unify the caucus, West Virginia Sen. Joe Manchin said.
"Her and Bernie were good," Manchin said. "Being there together. That was a good moment for the caucus. Pleasantries about everyone coming together and she has a plan forward."
As Clinton exited the meeting, she did not respond to questions about Indiana Gov. Mike Pence, who is rumored to be
Donald Trump's preferred running mate.
With several possible vice presidential candidates of her own at the meeting, Clinton was asked but didn't answer questions about whom she would pick to be her running mate.