Enrique departed his position following the disappointment of the 2022 World Cup, with La Roja being eliminated in the last-16 stage of the competition in Qatar.
Manchester United goalkeeper David de Gea has again been overlooked, but there is a spot in the squad for Chelsea's Kepa Arrizabalaga, with number one Unai Simon out through injury.
De la Fuente has kept just 11 members of the squad from the World Cup, meaning that there are 15 new faces in the selection following the competition towards the end of last year.
There are three uncapped players in the squad, with Real Sociedad's Martin Zubimendi, Osasuna's David Garcia and Espanyol's Joselu rewarded for their strong form this season.
"Our goalkeeper Unai Simon is out injured. We wish him a speedy recovery," De la Fuente told reporters on Friday. "Kepa is the most experienced of the three [Raya and Sanchez] but they will have to earn their place.
"We will look at how they do on a daily basis before deciding who starts. All three are very good and I'm sure whoever plays will do well. When selecting this squad, I have not looked at the past but rather at the present and the future."
Iago Aspas has found the back of the net on 11 occasions in La Liga this season for Celta Vigo, and the 35-year-old has also been brought back into the squad.
Barcelona's Pedri was initially named in the squad, having made excellent progress in his recovery from a hamstring issue, but the midfielder has suffered a setback - ruling him out of Sunday's El Clasico - which has seen him withdraw.
"The national coach, Luis de la Fuente, has unsummoned Pedri for the next few matches of the Spanish National Team after the conversations held between the medical services of the Royal Spanish Football Federation and Barcelona," read an official statement from Spain.
Gavi and Alejandro Balde are therefore the only Barcelona players in the squad, while Real Madrid have three representatives in the shape of Nacho, Dani Carvajal and Dani Ceballos.
Sergio Busquets has now retired from international duty, while Jordi Alba, Koke, Marcos Llorente, Ferran Torres, Marco Asensio and Ansu Fati are among the notable absentees.
Spain will take on Norway in their first Euro 2024 qualification fixture on March 25 before continuing their Group A campaign against Scotland three days later.
Full Spain squad
Goalkeepers: Kepa Arrizabalaga (Chelsea), Robert Sanchez (Brighton & Hove Albion), David Raya (Brentford)
Defenders: Jose Gaya (Valencia), Alejandro Balde (Barcelona), Aymeric Laporte (Manchester City), Inigo Martinez (Athletic Bilbao), Nacho (Real Madrid), Dani Carvajal (Real Madrid), David Garcia (Osasuna), Pedro Porro (Tottenham Hotspur)
Midfielders: Rodri (Manchester City), Martin Zubimendi (Real Sociedad), Mikel Merino (Real Sociedad), Gavi (Barcelona), Fabian Ruiz (Paris Saint-Germain), Dani Ceballos (Real Madrid)
Forwards: Alvaro Morata (Atletico Madrid), Dani Olmo (RB Leipzig), Nico Williams (Athletic Bilbao), Bryan Gil (Sevilla), Mikel Oyazarbal (Real Sociedad), Iago Aspas (Celta Vigo), Joselu (Espanyol), Gerard Moreno (Villarreal)