One of Baylor's position groups did not meet the thresholds for competition, according to a source.
The schools have agreed to honor their home-and-home agreement and monitor dates for future scheduling opportunities.
"The loss of this game is a devastating blow, but in the interest of the health and safety of our student-athletes, we believe we made the necessary decision," Baylor athletic director Mack B. Rhoades said in a statement.
"We are incredibly disappointed with the continued delay to the start of our season and empathize with our student-athletes, fans, coaches and administrative staff. We are grateful for the support and understanding of the University of Houston, athletic director Chris Pezman and Chancellor [Renu] Khator. We look forward to a future home and home matchup."
The schools worked quickly to schedule the game last week after previous postponements. Houston had been set to face Memphis on Friday night, but a rise in positive coronavirus tests at Memphis forced a postponement. Baylor's original season opener, Sept. 12 against Louisiana Tech, was postponed because of a COVID-19 outbreak at Louisiana Tech.
Baylor, under first-year coach Dave Aranda, must now prepare for a fourth potential season-opening opponent, as it initially had been set to face Ole Miss before the SEC went to a conference-only schedule. The Bears are set to host Kansas on Sept. 26, and Houston is set to host North Texas the same day.
"We're heartbroken from this postponement," Aranda said. "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."