The German jobless rate, which measures the proportion of people registered as unemployed against the working population as a whole, fell to 6.7 percent in May from 7.0 percent in April.
The data were provided on a raw or unadjusted basis by the Federal Labour Agency in Nuremberg.
In concrete terms, the total number of people out of work declined by 108,046 in May from April to stand at 2.855 million, the agency said in a statement.
Unemployment tends to fall in the spring as sectors such as the construction sector take on workers again with the end of the cold winter weather.
However, seasonally-adjusted numbers, which iron out such distortions, showed no change in the jobless total at 2.872 million in May compared with April, and the seasonally-adjusted jobless rate eased only slightly to 6.7 percent from 6.8 percent.
"The labour market continued to develop positively overall, but the positive trend is losing momentum," said the head of the Federal Labour Agency, Frank Weise.
While the German economy, Europe's biggest, dodged recession and grew by 0.5 percent in the first three months of this year, "the risks resulting from the European debt crisis have increased," Weise said, pointing to falling business and investor confidence.
Analysts, too, are beginning to see cracks in the dam wall that has so far shielded Germany from the worst of the storms lashing the single currency area.
"At first glance, today's numbers illustrate the strength of domestic demand, at least partly cushioning the German economy against the negative impact from the debt crisis," said ING Belgium economist Carsten Brzeski.
"At second glance, however, signs are increasing that the resilience of the German labour market is slowly cracking up," he said.
The usual May upturn in the labour market was the weakest it has been since 2002.
Moreover, companies are down-scaling their recruitment plans, the analyst said.
"The German labour market is losing momentum but this is not yet a cause for concern. At least not for this year. With a new boost from latest wage settlements, domestic demand might not be a strong, but definitely an important, growth driver," Brzeski said.
Newedge Strategy's Annalisa Piazza similarly believed that while the German labour market "remains solid ... companies are more cautious with their hiring plans as risks of spill-over effects from the eurozone debt crisis are looming."
Looking ahead, the jobless rate was unlikely to decline any further, she predicted.
Christian Schulz at Berenberg Bank also believed Germany's job market "is showing signs of slowing, although positive trends persist."
"In the short-term, the euro crisis is likely to weigh on the labour market. Once the crisis is brought back under control, however, the positive fundamental situation of the economy will lead to further increases in employment again," he predicted.