The Gunners captain will sit out his country's upcoming games against Faroe Islands and Scotland having recently suffered from a hip problem, as well as a concussion following a training ground accident.
It is expected that Odegaard will be ready for Arsenal's trip to Brentford after the international break.
Solbakken has also confirmed that the Premier League title challengers had long planned for their midfielder to miss this period of Norway games.
"We have known for quite some time that Martin will not come," he told reporters.
"But it must be coordinated with Arsenal, and for as long as they tried to get him healthy and ready, we were quite sure that it would not work.
"When the club is so reserved, I don't know how right it is for me to talk about it. It is a common football injury from which he will probably recover very well and which is not career-threatening. It is in the bone."
Odegaard, 24, will still join up with the Norway squad this week.
"He will have an individual training program for a few days," Solbakken said. "Then we hope that he will join the squad and watch the Faroe Islands match and be with us all of Friday."
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