Eric Bailly has also not travelled to Russia due to the one-match suspension that he earned as a result of his dismissal in United's last European match, away to Saint-Etienne.
Bastian Schweinsteiger has similarly stayed at home as he continues to recover from a minor injury.
Henrikh Mkhitaryan returns to the squad, in what will be a significant boost for the side, and could feature for the first time since suffering an injury moments after scoring the only goal in last month's win in France.
Mourinho and his men flew out from Manchester Airport on Tuesday afternoon ahead of their last-16 first-leg clash with the Russian side at the Olimp-2 Stadium.
Despite both starting for United in Saturday's 1-1 draw with visitors Bournemouth, Shaw and Rooney will not play a role in Thursday's clash.
There is no official indication that either of the pair are injured, or whether they have been simply overlooked by Mourinho.
Manchester United's 20-man squad: De Gea, Romero, O'Hara; Valencia, Jones, Rojo, Smalling, Blind, Darmian, Young; Carrick, Herrera, Fellaini, Pogba, Mata, Lingard, Mkhitaryan; Martial, Rashford, Ibrahimovic.Reuse content