The 3.1 percent voter support is the lowest in 35 years.
"It is definitiely a signal that the party has problems when the levels have also gone down in rural areas, where traditionally they had strong support," Ipsos analyst David Ahlin told the Dagens Nyheter (DN) newspaper, which commissioned the latest opinion poll.
"It is less than half the support compared to elections in 2010," Sveriges Radio (SR) said in an analysis on Friday.
Sweden enforces a four-percent minimum for a party to take seats in the national parliament. The minority Christian Democrats, one of the Centre Party's partners in government, also failed to attract enough support in the opinion poll to retain its parliamentary presence. With their bigger coalition partners - the Liberals (Folkpartiet) and the Moderates - the government has 39.7 percent of voter support at present.
"I take these figures seriously," party leader Annie Lööf told SR in Malmö. "Traditionally we are not very good at keeping our voter support between elections but we are good at sprinting when elections come up."
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Pressed to answer why voter support had decreased, Lööf reiterated that her party traditionally slumped between elections. She said she had never considered stepping down.
"The thought has never occurred to me. I'm here to win elections," Lööf said.