The pair have both been struck down by knee injuries, with Silva possibly out for two weeks.
"It is a big problem," said manager Roberto Mancini. "Neither of them will be available."
Silva in particular will be a huge loss at the Emirates given his growing influence on the Blues in recent weeks.
"David has been an important player for us and has been doing well recently," said Mancini. "Hopefully, he will be back for the Wolves game on January 15. Mario might be back for the FA Cup tie at Leicester on Sunday."
Mancini also confirmed he is confident of securing the services of Bosnian striker Edin Dzeko from Wolfsburg, adding: "We have agreed a fee. He is a good player and all the teams in Europe want him. But we have an important game at Arsenal coming up and I will speak about him after that."