The 28-year-old was named in Zinedine Zidane's 24-man group for the game at Estadio Manuel Martinez Valero.
Zidane hinted he would give Isco minutes as part of his squad rotation, with the 28-year-old being restricted to only three starts in all competitions this term.
"Isco is not part of the Real Madrid travelling party for tonight's LaLiga Matchday 16 encounter against Elche at the Martinez Valero," a club statement read.
"The Malaga-born man was initially named in Zinedine Zidane's 24-man squad but is a last-minute withdrawal after becoming a father."
Isco has been strongly linked with a move away from Madrid in the January window after being used only 11 times in all competitions this term.
Arsenal are rumored to be weighing up an initial loan deal for the playmaker, who has no goals and one assist in 10 LaLiga outings in 2020-21, just three of those being starts.
Isco averages 1.65 chances created per 90 minutes in LaLiga since the start of last season, putting him behind Toni Kroos (2.22), Luka Modric (1.84), Lucas Vazquez (1.8) and Rodrygo Goes (1.69) among Madrid players to have played at least 10 times.
In his seven and a half years in Madrid, meanwhile, only Karim Benzema (60), Cristiano Ronaldo (47) and Toni Kroos (46) have provided more LaLiga assists for Los Blancos than Isco (42), who has created 306 chances in 217 matches (1.4 per game).
Madrid make the trip to Elche sitting level on points with leaders Atletico, who have two games in hand to play.
Eden Hazard is among those in contention to play a part in the Spanish giants' final game of 2020 after recovering from his eighth injury layoff in 16 months.