The Arsenal and Norway captain suffered a knee injury during victory over West Ham on the weekend.
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And Engebretsen told Dagbladet: "I don't have information about exactly what the MRI showed but based on the injury video, it could be a lateral ligament injury.
"If it is such an injury, Odegaard risks being out for six to eight weeks but it depends on the size.
"It could also be a more extensive injury, cruciate ligaments maybe. In that case, the period on the sidelines could be longer."
Odegaard set a new Premier League record when he was substituted against West Ham, becoming the first player to be withdrawn before half-time in three consecutive matches.