Arnautovic limped off late in the first half of West Ham's Premier League win at home to Cardiff City, in which his replacement Lucas Perez scored twice.
The Austria international appeared to pull his hamstring and announced his injury setback in a social media post the day after the Cardiff win.
"Thank you so much for all your messages," Arnautovic wrote on Instagram. "I will be out for a while, but I will do everything to come back strong and quick."
Arnautovic has been linked with a move away from West Ham, the 29 year-old's brother and agent Daniel naming Everton and Chelsea as potential suitors, with Manchester United also reportedly interested.
The 3-1 defeat of Cardiff saw West Ham follow up its win at Newcastle with another three points, moving Mauricio Pellegrini's side up to 12th in the table.
The Hammers host Crystal Palace in their next match with Premier League games against Fulham, Watford, Southampton and Burnley to come before next year.