The Norwegian superstar was substituted during a Nations League match against Austria following a harsh tackle that targeted his ankle.
Norway's team doctor Ole Sand felt that he would be out for around three weeks.
He stated: “Such ankle injuries often take at least three weeks. Anything other than that is just a bonus. And then it can take longer."
He did add: "What we have so far obtained from the MRI examination in London is that there is probably no fracture in the ankle.”
Odegaard had a scan in Hertfordshire on Tuesday and Arsenal fans will hope the results are positive.