Xavi has been ruled out for 15 days with iliotibial band syndrome, an injury that is affecting his right leg, while Alonso has a groin injury.
Barcelona on Monday confirmed that Xavi will miss La Liga matches against Getafe and Granada but remains hopeful he will be fit to face Milan in the first leg of their Champions League last-16 tie at the San Siro on Feb. 20.
"If his recovery goes as planned, he'll be back for the Champions League game against Milan set for 20th of this month," a club statement read.
Xavi has made 33 appearances this season and scored six goals.
Vicente Del Bosque's main striking options for the Uruguay match are Alvaro Negredo and Spain's record goalscorer David Villa, who has been named in the squad despite not being a regular in the Barcelona lineup since returning from his serious leg injury.
Azpilicueta, Torres' Chelsea teammate, could be in line to make his first Spain appearance against Uruguay.
Carles Puyol, who has not played for his country since last February because of injury, also made the trip and would make his 100th appearance for the world and European champions if he takes the field in Doha.
Captain and goalkeeper Iker Casillas will miss the match with a broken hand, while recent call-ups Jesus Navas, Roberto Soldado, Raul Albiol, Benat Etxebarria, Martin Montoya, Markel Susaeta and Javi Martinez have all been omitted.
"I know it's a friendly game and that we could have experimented more but we need to use this match as a preparation game, because in March we face two very difficult games," Del Bosque said. "We have to treat it with the utmost seriousness, because we are also facing an opponent in Uruguay who are the South American champions, who reached the World Cup semifinals and are fighting to qualify for Brazil 2014."
Spain is currently top of its World Cup qualifying group but only on goal difference from France, which it faces on the road in March.