The Austria international will miss most of the Christmas period, although the club are hopeful he will return for the FA Cup third round tie against Birmingham in January.
“We know how important Marko is for our team,” said West Ham boss Manuel Pellegrini.
“We have too many players injured in a month that we have to play seven games and then in January, six more games.
“But I always have the same answer - we have a squad and it is a chance for another player to demonstrate why they are here.”
Arnautovic joins Jack Wilshere, Andriy Yarmolenko, Ryan Fredericks, Carlos Sanchez, Aaron Cresswell, Winston Reid and Manuel Lanzini on a lengthy casualty list.
But defenders Pablo Zabaleta and Fabian Balbuena are available after missing the midweek win over Cardiff.
Provisional squad: Fabianski, Adrian, Zabaleta, Balbuena, Diop, Ogbonna, Masuaku, Rice, Obiang, Noble, Diangana, Snodgrass, Anderson, Antonio, Hernandez, Carroll, Perez, Silva.