The contest is being delayed because the Bears don't meet the Big 12's COVID-19 game cancellation thresholds.
"We're heartbroken from this postponement," said Bears head coach Dave Aranda. "While we've been eager to play football this fall, we have all made a commitment to only do so with the highest level of safety and care for our student-athletes. We are disappointed for our team, staff, and our fans, but look forward with great anticipation to renewing this rivalry in the future."
Both Baylor and Houston have agreed to honor the future home-and-home schedule.
The Bears informed the Cougars on Friday that positive COVID-19 test results and contact tracing put their offensive line below the conference's minimum threshold to play, sources told Ross Dellenger of Sports Illustrated.
The contest was only scheduled last week after the Cougars' game with Memphis was postponed due to a COVID-19 outbreak within the Tigers' program.
Baylor's planned season opener against Louisiana Tech was also pushed back due to a coronavirus outbreak on the Bulldogs in which 38 players reportedly tested positive.