Only 12.6 percent of the 1,000 people surveyed last week said they were in favour of joining the 27-member bloc, while 7.6 percent were undecided, according to the poll conducted by the Sentio institute and published in the daily Nationen.
Opposition to EU membership has never been as high in Sentio's surveys of the oil-rich Scandinavian country, which has twice rejected membership in referendums in 1972 and 1994.
"It is difficult to imagine anything other than that it is linked to the crisis," a senior official at the employers' organisation Confederation of Norwegian Enterprise, Peter Haas Brubakk, told Nationen.
"In addition, no party nor public figure is currently talking about Norwegian EU membership as being an important issue," he added.
The centre-left government coalition in power is divided on the question and has put the issue on the back burner.