Merkel's conservative Christian Democrats, CDU, are facing off against the Social Democrats, SPD, for the top spot in Hesse, home to Germany's finance capital Frankfurt, and 4.4 million people are called to the polls.
Surveys predict a clear win for the chancellor's party.
The conservatives and the SPD have been bound together at the national level in a fractious “grand coalition” since 2005 and are now together grappling with the country's worst post-war recession.
But with 16 elections planned this year on regional, state, national and European levels, the trick has been to press on with the business of running Europe's biggest economy at the same time they battle each other at the polls.
The awkwardness of this arrangement was underlined this week at two joint appearances between Merkel and her Social Democratic challenger in September, Foreign Minister Frank-Walter Steinmeier.
They came together at a news conference and before parliament to defend a new €50 billion economic stimulus package hammered out by their two sides in a bid to pull the German economy out of the mire.
Merkel told a CDU campaign rally in Frankfurt late on Friday that Germans should see the crisis as a chance to invest in the future.
“We are using the crisis as an opportunity to modernise our infrastructure, education and training and child care facilities,” she said.
“We are facing a global economic crisis and we must summon all our strength to lead our country out of this crisis.”
However a poll published in the Bild am Sonntag newspaper indicated that Germans are highly sceptical about the measures, with 90 percent saying they doubted whether they would personally benefit from the plan.
Meanwhile 61 percent doubted that the package would help end the recession, according to the survey of 1,003 people conducted by the independent TNS-Emnid institute.
Despite the crippling slowdown, the Christian Democrats appear not to be paying the price with voters for their role as senior partners in the federal government, thanks in large part to internal squabbling among the Social Democrats.
Opinion polls suggest that Merkel's conservatives will win re-election in Hesse with more than 40 percent of the vote and secure a decisive ruling majority with their preferred partners, the pro-business Free Democrats, FPD.
The SPD, polling at less than 25 percent, look set for a historic defeat.
Hesse is already scorched earth for the SPD after an inconclusive election a year ago.
The SPD's chief candidate Andrea Ypsilanti wanted to form a coalition with the Greens but also rely on the far-left party Die Linke for votes - breaking a campaign pledge not to work with the outfit.
The bid failed when four rogue Social Democrats withdrew their support, saying their consciences would not allow them to vote for the new government.
The SPD's dealings with the Die Linke, a loose-knit grouping of former East German communists and disaffected Social Democrats, have taken on a national dimension, helping lead last year to the ouster of party leader Kurt Beck.
Steinmeier has ruled out working with the Die Linke on the federal level but has given his blessing to coalitions at state level.
This time Die Linke risks falling short of the five-percent hurdle required for representation in the Hesse state legislature.
Exit poll results are due at 6pm with preliminary official results expected soon after.