Trust in Lööf's leadership has sunk 5 percent since last year, according to results of a Sifo Institute opinion poll ordered by the tabloid Aftonbladet.
A year ago, when she was relatively new in the job, Lööf had a third of voters' confidence.
A Centre Party representative told The Local there would be no official comment on the latest opinion poll.
It is a historic low for the party as no other leader has had such dismal voter support since Aftonbladet began its series of Sifo polls 17 years ago.
The 30-year-old politician has also seen support for her leadership among her party's voters fall.
Nine percent say they have either "confidence" or "high confidence" in Lööf. That figure is down 19 percentage points since the last poll.
Many Centre Party supporters were hoping that Lööf, who also took on the job as enterprise minister in September 2011, would inspire an upswing in voter support or even attract new voters.
But any "Lööf Effect" is not discernible in the polls, which also show that if elections were held today, the Centre Party would get 3.9 percent of the votes.
As there is a 4-percent threshold to get into parliament it would wreak havoc on the party and endanger the government coalition.
The prime minister, however, still enjoys the highest confidence rating of all the political party leaders. Fredrik Reinfeldt today has 62 percent of voters' trust while 48 percent of Swedes feel confidence in his main antagonist, opposition Social Democrat leader Stefan Löfven.
The leader of the anti-immigration Sweden Democrat party, Jimmie Åkesson, has the lowest confidence rating at 12 percent.