The poll from Synovate is the first which shows that four parties, two in government and two in opposition, would fall below the 4 percent threshold.
The greatest drop is recorded by the Sweden Democrats, which fell from 4.8 percent in June to 2.9 percent in the poll, which represents a loss of 40 percent of its sympathizers.
According to Synovate's analyst Nickals Källebring, the dramatic fall can be explained by the twin terror attacks in Norway and ensuing controversy over comments by some SD party members.
"It is a direct effect of the fatal shootings on Utøya. I can't interpret the decline in any other way."
The Christian Democrats fell 1.2 percentage points and claimed 3.3 percent in the poll, grim news for under-fire party leader Göran Hägglund who faces a further test of his leadership at the party congress in January.
Alliance coalition government colleagues the Centre Party fell to 3.8 percent, coming in below the threshold for the second consecutive time in a Synovate poll.
Doubts over policy and the ongoing search for a new party leader has meant that voters are uncertain as to where the Centre Party stands or it is headed, according to Källebring's analysis.
The big winners in the poll are the Moderates, who climbed sharply by 4.5 percentage points to 36.9 percent, explained as a result of a renewed focus on the economy.
The party is back on the same levels of support that it enjoyed in the period immediately after the election and during the turmoil of Mona Sahlin's departure as head of the Social Democrats.
The Social Democrats meanwhile held their ground on the previous poll in May, polling 32.8 percent.
The Green Party polled 8.4 percent, down 1.9 percentage points on May.
The changes to the Moderates and the Sweden Democrats are the only statistically significant changes in the poll.
The Moderates advance means that the government Alliance coalition significantly increases its lead over the opposition, with the gap stretched to 6.6 percent.
The government parties are now on 51.5 percent to 44.9 percent for the red-green opposition.