Brazilian forward Rodrygo Goes also misses out on the 19-man squad, along with Brahim Diaz and Nacho Fernandez.
Head coach Zinedine Zidane had suggested Bale and Hazard could be involved in the match at the Santiago Bernabeu after some encouraging signs in training this week.
Hazard has been out since November with an ankle injury, while Bale was hurt in the 3-1 Copa del Rey triumph over Unionistas de Salamanca last week and missed wins over Real Valladolid and Real Zaragoza.
Bale had been linked with a deadline-day return to Tottenham but Zidane insisted on Friday he was "not contemplating" such a move.
Casemiro, Eder Militao and Isco have all returned to the Madrid squad for the clash with Diego Simeone's side.
Madrid are three points clear at the top of LaLiga after 21 matches, 10 points above Atleti, who sit in fifth place.