The teams were scheduled to play Saturday at Folsom Field. A makeup date has not been determined.
The area has been hit hard by torrential showers, leading to flooding in northern Colorado, especially mountain communities around Boulder. The university has canceled classes through at least Friday after approximately 40 buildings suffered water damage. Students in family housing near Boulder Creek were also forced to leave.
"Even though the weather is improving, Boulder is still designated as a national emergency site," University of Colorado-Boulder chancellor Philip DiStefano said. "Our community is hurting. Many of our students are displaced from their homes, including many of our student-athletes. This is not an appropriate time for us to hold a game that would put pressure on the community, both in terms of security/emergency personnel, but also in diverting attention from people in need."
DiStefano also said that "ensuring the safety of CU affiliates and fans has always been the No. 1 priority."
Colorado coach Mike MacIntyre said the team has moved several players into hotels after they had to leave their homes because of flooding.
"There are a lot issues out there that are a lot bigger than football," MacIntyre said. "This is the appropriate decision, and we are all 100 percent in agreement.
"They will be ready to play whenever we get back on that field again. I promise you, we'll be ready to go."
Athletic director Rick George said in a conference call Friday that he will begin discussing the options of rescheduling the game with Fresno State in the next few days. The contest could be made up at the end of the season or possibly even canceled altogether if no dates work out.
Fresno State opens Mountain West Conference play next week against Boise State, while the Buffs begin Pac-12 play at Oregon State on Sept. 28.
"While we're disappointed we're not going to get the opportunity to play against the University of Colorado, we understand the tragic situation there and we send our thoughts and prayers out to the people of Colorado and wish them the best in their recovery efforts," said Fresno State coach Tim DeRuyter, whose team entered the week on the verge of being ranked in the AP Top 25 poll.
Up the road in Fort Collins, the game between Colorado State and Cal Poly still will be played Saturday.
With rain still falling as of Friday morning and the flood threat still real, authorities called on thousands of people in the inundated city of Boulder and nearby towns to evacuate as rivers and creeks rose to dangerous levels.
At least three people were killed, and numerous people were forced to seek shelter up and down Colorado's populated Front Range. Boulder County spokesman James Burrus said 17 people were unaccounted for as of Friday morning.
President Barack Obama signed an emergency declaration Thursday night, freeing federal aid and allowing the Federal Emergency Management Agency to coordinate disaster relief efforts.
Brett McMurphy of ESPN.com contributed to this report.