The Arsenal skipper left the pitch after receiving treatment for several minutes in the second half following a collision with Austria's Christoph Baumgartner, and Norway boss Stale Solbakken said it looked bad.
"Martin Odegaard's injury looked bad in the dressing room as well I saw he was sitting with the physiotherapists around him but he had no chance to continue and we know it was an ankle sprain," the coach said to Norwegian TV 2.
"Yes it's a sprain, and as those of us who had played football know, with luck it can turn out ok if the ligaments aren't torn."
Norway's doctor Ola Sand added that the 25-year-old was doing well, but that an MRI could be carried out tomorrow.
"Martin is doing quite well now. He got a small ankle sprain. We will see throughout the evening and tomorrow what happens next and what we will do about it.
"Ankle sprains are difficult to deal with straight away, so we almost have to see how things go forward. We will examine him when we are back at the hotel. Maybe we use ultrasound to look at it. If we are unsure, there will be an MRI tomorrow," Sand said.
Norway are second in League B Group 3, level on four points with Slovenia, who they will play next on October 10.
If the injury proves to be serious, Odegaard will miss a key run of games for Arsenal with the next three being against Tottenham, Atalanta and Manchester City.