Muentefering, 67, who is also the labor minister, is stepping down "for purely family reasons," a Labor Ministry spokeswoman said on customary condition of anonymity. The ministry did not elaborate, but Muentefering's wife has cancer and recently underwent an operation.
Muentefering planned to make a statement on Tuesday afternoon, the ministry said.
There was no immediate word on who would replace Muentefering, a Social Democrat who has worked well with Christian Democrat Merkel at the head of the often-fractious coalition of Germany's biggest parties that emerged from an indecisive 2005 election.
Muentefering will be the first minister to depart Merkel's government, two years into its four-year term.
Muentefering had cut a somewhat isolated figure in the Social Democrats, the party of former Chancellor Gerhard Schroeder, over recent months as the party sought to strengthen its left-wing credentials to claw its way out of a poll slump.
Muentefering was a key ally of Schroeder in pushing through the former leader's so-called "Agenda 2010" of economic reforms, and had opposed a push by party chairman Kurt Beck to soften one of those reforms by expanding jobless benefits for older unemployed people. Early on Tuesday, coalition leaders agreed to that expansion.
Beck, who took over as the leader of the Social Democrats last year, is seen as the likeliest challenger to Merkel at Germany's next election, due in 2009. He currently holds no federal government post, and has kept his job as governor of the western state of Rhineland-Palatinate.
The Social Democrats hold half of the 16 posts in Merkel's Cabinet after finishing only just behind her conservative bloc in the 2005 election.