The poll, for public TV channel ARD, put Merkel's centre-right Christian Democrats (CDU) and Bavarian sister party CSU at 39 percent of the vote, its highest level since March 2008.
The main opposition party, the centre-left Social Democrats (SPD), would win 31 percent of the vote in an election, said the poll, a gain of one percentage point since the last poll.
Last Friday, the SPD nominated former Finance Minister Peer Steinbrück as its candidate to challenge Merkel in national election, to be held in September or October next year.
But the poll also suggested he has an uphill task to unseat Merkel.
If Germans could vote directly for their leader, 49 percent would vote for Merkel and 38 percent for Steinbrück.
Merkel remains the country's most popular politician, as Germans approve of her handling of the eurozone debt crisis.
Two-thirds of Germans said they are satisfied with her work. In second place is Finance Minister Wolfgang Schäuble with 64 percent.
Steinbrück came third in the popularity stakes after 59 percent of people said they were satisfied with his work – a gain of nine percentage points compared to the previous month.
The challenger has been beset since his nomination with criticism over money he received for making speeches.
The survey put Merkel's junior coalition partner, the pro-business Free Democrats, at four percent of the vote, not enough to win parliamentary seats.
The ecologists Greens polled 11 percent and the far-left Linke party seven percent.
The upstart Pirate Party, which campaigns for Internet freedom, continued to see its star wane, registering four percent of the vote after approaching a double-digit level of support earlier in the year.
ARD interviewed 1,501 people for the survey between October 1 and 3.