Zimmerman, 30, was an aide to Rep. Gabrielle Giffords, who was hosting an event in a Safeway parking lot when a 22-year-old man opened fire. Twenty people were shot, including six who died, the Pima County Sheriff's Department said.
The two UCSC alumni who established the scholarship fund - Alex Clemens and Jonathan Klein - have no relationship to Zimmerman, but they received approval from the shooting victim's family.
Clemens said that, based on what he knows about him, Zimmerman was a shining example of what it takes to work in politics.
"He embodied the traits you want to see for a person who goes into public service," he said.
Clemens, who has worked as an aide in San Francisco and Washington, D.C., said he is deeply saddened by the events in Arizona and hopes the fund will provide an outlet for people who are hoping to speak out against shootings.
The fund has had a Facebook page since about noon today and has already garnered more than $3,000 through Facebook donations, he said.
Those interested in donating should search on Facebook for "Zimmerman Scholarship," Clemens said.
The donation page already has more than 50 people following it.
UCSC has been coordinating its own donation efforts, and word of the fund has already spread, said Joop Rubens, UCSC's director of philanthropy.
"I have been working 20 hours straight trying to respond to people," Rubens said.
He said many people have been eager to donate because of their previous relationships to Zimmerman.
One donor, Colin Pyle of Scotland, was studying abroad at UCSC when Zimmerman attended. He contributed $100 to the scholarship fund.
"He was a roommate with a good friend of mine," Pyle said in a letter to the fund. "Gabe signed me up for the College Democrats."
UCSC alumna Margaret Bowe contacted the school with interest in the fund because she was friends with Zimmerman during her freshman year.
"He was such a warm, funny, energetic, smart, interesting person who was passionate about life," she said. "Being his friend was the easiest, most natural, and only thing to do once you met him."
Rubens said interest in the fund has come from as far away as Australia.
He said the university aims to raise $50,000, and officials are trying to accomplish their goal in only a matter of days.
"I feel there's a sad risk that interest on this issue will dwindle, and I really want to keep the focus on this," Rubens said. "The way we can ensure that Gabe Zimmerman's memory is eternalized in endowing a scholarship fund."
Those who wish to donate directly through UCSC can visit http://giving.ucsc.edu and click "Make a Gift Now."