The 25-year-old scored twice in his country's 8-0 win over San Marino on Thursday but came off around the hour mark.
King, who has scored five times in the campaign, has now confirmed that he will not be risked for Sunday's encounter in Oslo.
"I felt my hamstring during the game and in view of my history, we do not take any chances," King told Norwegian outlet NFF TV.
"Myself, Lars [Lagerback] and the medical team have discussed and agreed that I'm going home to get back [to fitness] as early as possible."
King, whose nation is out of contention to reach Russia, is also believed to be a doubt for Bournemouth's next Premier League match against Tottenham Hotspur next Saturday.