Sinn Féin leads Fine Gael by 10 points, according to the latest Sunday Times opinion poll.
Leo Varadkar's party has dropped two points to 23% - while Mary Lou McDonald's is up three, at 33%.
It's the first poll since Mr Varadkar and his Fine Gael colleague Simon Coveney became embroiled in the controversy over the appointment of Katherine Zappone as a UN special envoy.
There's been little change elsewhere in the Behaviour & Attitudes poll, with Fianna Fáil up one point to 21%, and Labour and Greens unchanged at 5% each.
Meanwhile, Tánaiste Leo Varadkar's personal satisfaction rating has also fallen by nine points, to 39%.
Mary Lou McDonald remains the most popular party leader, with a 48% satisfaction rating (down one point on the last poll).
Satisfaction ratings have remained unchanged for Fianna Fáil's Micheál Martin (45%) and Labour's Alan Kelly (44%), while Green leader Eamon Ryan's rating has risen by two points to 34%.
However, the poll shows overall satisfaction with the Government has fallen by four points to just 42%.
Stephen O'Brien, the political editor of The Sunday Times, says there's an obvious reason for Leo Varadkar's drop in popularity.
He said: "The context is [the poll's] coming after what has been a difficult summer for Fine Gael, following the controversy over the appointment of Katherine Zappone as UN special envoy.
"The other controversy, I guess, involving the Tánaiste was he was photographed at a live open-air concert in London... he drew some criticism from opposition parties about that, as the Electric Picnic had just been cancelled here in Ireland."
