Midfielder Odegaard underwent an MRI scan after sustaining the injury in a challenge by Austria's Christoph Baumgartner in Norway's 2-1 victory over the Austrians in Oslo on Monday.
"This type of ankle injury often takes at least three weeks to heal. Anything less is just a bonus. And it may take longer," national team doctor Ola Sand told the VG newspaper.
Norway's next Nations League matches are on October 10, against Slovenia in Oslo, and then against Austria three days later in Linz.
"Both Staale (Solbakken, the coach) and I know that this is delicate," Sand said.
"It's not out of the question (that he plays), but we have to wait and see what the MRI says and how quickly he responds to treatment."
Sand added the MRI images were still being studied, although there was "no suspicion of a fracture".
At club level, Odegaard risks missing Arsenal's opening Champions League matches against Atalanta on September 19 and Paris Saint-Germain on October 1.
