Northug, 32, won two golds, a silver and a bronze at the 2010 Winter Games and has 13 World Championship titles, but he has been in poor form lately.
"He's been sick a lot and not taken part in many races," the head of the Norwegian Olympic Committee, Tore Øvrebø, said.
"And he hasn't been that fast in the ones he has taken part in. So, ultimately, he didn't make the team," he told a press conference.
Northug skipped a World Cup race in Slovenia last weekend after coming down with the flu, reducing even further his chances of being selected for Pyeongchang, though Norway's Olympic Committee had not totally ruled it out.
"There were doubts up until the end," Øvrebø said.