"He's stressed by his situation, that's why I've chosen to overlook him this time," Olsen told reporters.
The 31-year-old has suffered from a loss of form and a lack of playing time since moving to Liverpool from Juventus a year ago.
"We hope that Christian finds a good club and gets playing time so that he can return against Portugal and Cyprus in October," the coach said, adding that Poulsen's Liverpool team-mate Daniel Agger will wear the captain's armband in his absence.
Portugal, Denmark and Norway all have 10 points in Group H, with the Portuguese top on goal difference.
Norway face Iceland on September 2 before travelling to Copenhagen to take on the Danes four days later.
'Ludicrous' Neymar clause revealed as Barcelona permitted Brazilian surprise luxury once a month
'I can actually assure you Mohamed Salah has been offered a contract! I'd also be looking at them like, why haven’t you signed? The team is made for them, where are they gonna go?': Liverpool icon shares view on star's situation
