It is the third long-term injury suffered by a Hull player this season as both goalkeeper Allan McGregor and defender Alex Bruce also face lengthy injury lay-offs.
"First and foremost, it's desperately disappointing news for Moses," said Hull manager Steve Bruce.
"He was exceptional for us last season as we won promotion back to the Premier League and we expect him to be a top player for many years to come.
"I know how much he was looking forward to testing himself in the top-flight of English football and to now have to sit out the first half of the season is a big blow for him and for the club".