The decision comes after the teams' most recent game ended in controversy when BYU freshman Nick Emery punched Utah guard Brandon Taylor late in the game. Emery was ejected and given an automatic one-game suspension.
"The events that have occurred in our recent games with BYU led me to ask [athletic director] Dr. Hill several weeks ago if we could take a cooling off period and put the rivalry on hold," Utah coach Larry Krystkowiak said in a statement. "The level of emotions has escalated to the point where there is the potential for serious injury. Chris said he would support me in canceling next year's scheduled game against BYU. I called and let Coach [Dave] Rose know our intentions a few days after our game [on Dec. 2]."
Rose, though, said he wasn't on board with the move.
"I disagree with the decision," he said in a statement. "I know our students, our players, our fans and college basketball fans in the intermountain area want to see this long-standing rivalry continue."
BYU athletic director Tom Holmoe also called the cancellation "ridiculous" in a tweet Thursday.
Cancelling the BYU/Utah basketball series is RIDICULOUS. #letsplaythegame— Tom Holmoe (@TomHolmoe) January 7, 2016
Utah will pay an $80,000 guarantee fee for breaking the contract, according to Rose, who said the original contract was a four-year deal between him and former Utah coach Jim Boylen. Rose wanted a four-year deal with Krystkowiak, but Krystkowiak agreed to only two years, the first of which was this season.
Rose said he reached out to Krystkowiak to see if he could at least finish the series but was told no.
"I was very surprised. Shocked, actually," Rose went on to tell reporters Wednesday. "I've been doing this for 32 years in high school and junior college, now at the Division I level, and we've had hundreds of agreements on games. We've had verbal agreements, handshake agreements, and written contracts.
"This is the first time that I've had one not fully executed. I was surprised."
The teams have been playing each other since 1909. The lone year they did not meet was in 1944, when college basketball seasons were cut short because of World War II.
Utah has won the last three matchups. BYU, though, leads the series, 129-128.
BYU said it is moving forward with replacing Utah on its schedule for next season.
Hill said Utah would revisit resuming the rivalry "at some point in the future."
Information from ESPN.com's Andy Katz was used in this report.