The defender pulled up with a hamstring complaint and was forced off after just seven minutes of his side's opening Premier League defeat at home to Tottenham Hotspur.
Speaking after the game at St James' Park, Benitez told Sky Sports News: "We don't know [the prognosis]. It's too early. The main thing is we lost two players and we had to adapt.
"We have to wait but a couple of weeks, one of them, for sure. Maybe Dummett. I don't know."
Up next for Newcastle is a Premier League meeting with fellow newly-promoted side Huddersfield Town at the John Smith's Stadium in next Saturday's early kickoff.