The Spaniard walked off the pitch clutching his hamstring on Sunday after picking up the problem as he warmed up ahead of the Premier League clash at Old Trafford.
It means that Kurt Zouma will replace Alonso in Antonio Conte's starting line up, with the Italian likely to start Cesar Azpilicueta in the wing-back role as Zouma comes into his three-man defence.
Chelsea take on United hoping to restore their seven-point lead at the top of the table after Tottenham's 4-0 win over Bournemouth on Saturday cut the gap between second and first to four points.
Man Utd starting XI: de Gea, Valencia, Bailly, Rojo, Darmian, Fellaini, Ander Herrera, Pogba, Lingard, Rashford, Young
Subs: Ibrahimovic, Carrick, Blind, Romero, Mkhitaryan, Shaw, Fosu-Mensah
Chelsea starting XI: Begovic, Zouma, Luiz, Cahill, Moses, Kante, Matic, Azpilicueta, Pedro, Hazard, Costa
Subs: Fabregas, Loftus-Cheek, Willian, Batshuayi, Terry, Eduardo, Ake