Obertan pulled up on a sprint for the ball in the first half of Newcastle's 1-0 win over Liverpool at St James' Park on Saturday, and was substituted in the 27th minute.
The Frenchman, 25, scored just his second league goal for Newcastle in four seasons in their 1-0 win over Leicester in October, handing the club their first victory of the season and sparking a four-match purple patch.
The Mirror is reporting the former Manchester United man will be unavailable until the second half of the season.
Obertan's loss is likely to see manager Alan Pardew turn to Sammy Ameobi to fill the void after the exciting attacker gave fans a glimpse of his ability with his lightning quick goal from the second-half restart in their 2-1 win at Tottenham in October.
Ameobi, 22, made just his seventh league start for the club in their win over the Reds, having come through the youth set-up at St James'.
The winger, who has represented both Nigeria and England at under-age international level, said he is due to deliver on his untapped talent.
"I want to start for Newcastle every week, so I've got to make the most of this opportunity and make sure I don't slip up," Ameobi said.
"I'm not going to let that go this time. I'm not a kid anymore, and I realise that.
"It's one thing being told you have all this talent, but I'm at an age when I have to produce it.
"I'm a grown man and it's not about potential anymore, it's about actually doing something.
"I have to start playing like a man and acting like a man, and hopefully this season can be the start of that."
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