According to reports, Hazard's wife, Natacha, gave birth to a boy late on Friday.
The Belgium international was excluded from the 19-man travelling list released ahead of Madrid's flight out for Saturday's fixture.
Hazard's absence leaves Zinedine Zidane lacking two first-choice wingers, with Gareth Bale unavailable after limping through the final stages of Wales' 1-1 draw against Croatia last weekend.
Luka Modric suffered bruising to his right quadriceps in the same Euro 2020 qualifier and also misses the Mallorca match, as does Dani Carvajal.
Brahim Diaz and little-used striker Mariano Diaz will both hope to make their first appearances of the season.