He returned to action last week as a substitute in the UEFA Champions League defeat against Inter Milan before starting in the 1-1 draw at Chelsea on Sunday.
He travelled to Oslo to join up with Norway ahead of games against Slovenia and Kazakhstan, but has now returned to London.
“After discussions with the medical staff at the national team, we have unfortunately come to the conclusion that the situation is not good enough to play these games,” said Odegaard.
“I’ve been through a long training period and when you haven’t practised football in the last nine weeks, it’s natural not to be 100% yet. I need to listen to my body, complete this rehab process and get my foot back in good shape.
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“The hope has always been to be able to play the national matches, and if I hadn’t played on Sunday, it would have been out of the question to participate anyway.
“It’s a very bad feeling to lose these games, I love playing for Norway and with this team.”
Odegaard missed 12 matches for Arsenal following his injury in September and has only made five appearances in all competitions this season.
His return to London should be well received by Arsenal manager Mikel Arteta, who has spoken about dealing with an injury “nightmare”.
Norway team doctor Ola Sand said it was “too risky” for Odegaard to play during this international break.
“We examined Martin thoroughly last night, and we are certain that he is not match-ready.
“He has a complicated ankle injury and has trained very little in recent weeks. What we know is that a previous injury is often the precursor to a new one, so it’s too risky.
“He really wants to play for the national team, but from our standpoint, the two matches are completely unrealistic.”
Norway are top of Nations League Group B3 with seven points from four matches.
Arsenal’s next fixture is against Nottingham Forest on November 23.