Alt-right organization the National Policy Institute, of which Spencer is president, is paying the $10,564 to rent the UF space.
A law enforcement official said the man was being detained for having a firearm on campus.
The death in Charlottesville, home to the flagship campus of the University of Virginia, occurred as counter-protesters were dispersing.
Many churches and community centers held vigils to pray for peace and some students even gathered outside of the Phillips Center, where Spencer will speak today, to unite against his ideologies early.
Federal and local officials are bracing for potential protests during Spencer's scheduled speech, which have already begun.
"It's very tense and upsetting", Wes Li, a 20-year-old philosophy student, said of the speech.
A Penn State spokeswoman declined comment, pointing to an August statement in which Barron denied Padgett's request, citing concerns that a talk by Spencer could result in "disruption and violence".
As co-editor of AltRight.com and president of The National Policy Institute, white supremacist Richard Spencer has risen to become one of the highest profile white nationalists in America.
"Everyone is welcome at #SpenceratUF", he tweeted before the event Thursday. "This executive order is an additional step to ensure that the University of Florida and the entire community is prepared so everyone can stay safe".
Hundreds of police officers wearing bulletproof vests were deployed at the University of Florida on Thursday to guard against unrest over a speech by a white nationalist that was expected to draw thousands in protest.
Alachua County Sheriff's Office spokesman Chris Sims said the office used the lessons of Charlottesville in planning.
Mr Spencer said this week's emergency declaration by the state governor was "flattering" but "most likely overkill", reports the Orlando Sentinel newspaper.
Many on campus came ready to confront Spencer and his supporters, while other struggled with the best way to respond.
Weapons were been banned from the event, along with a wide range of other items, including water bottles, masks, shields and hats. "It is our creation and our inheritance, and it belongs to us", he said in a speech last November.