Some 19 firefighters were killed and more than 100 homes destroyed when the Yarnell Hill fire ripped through the community of about 650 people in June.
In making the request, Brewer said covering uninsured losses and restoring the water system would cost less than $20 million, KNXV-TV, Phoenix, reported Thursday.
Federal disaster relief would prevent the state would pulling from its reserves, she said.
"Such disaster relief would do so much for Arizona, not the least of which is help homeowners who lost everything," the governor said.
Yarnell resident Robert Westfall said the fire "basically took my life away" when his home burned down.
"I'm paying my taxes I live here, I would assume that when something like this happens and it's this bad that somebody's going to help and to this day we haven't gotten any," he said.