Analysts at financial services provider Factset had expected a drop of 5,000 people registered as unemployed from June.
It was the fifth month in a row that the seasonally adjusted rate -- which measures the jobless total against the working population as a whole -- stayed at 6.4 percent, the lowest level since 1991.
In raw or unadjusted terms, the jobless rate rose slightly to 6.3 percent from 6.2 percent in June.
That represents a total of 2.77 million unemployed -- up 61,000 from the previous month, many of them school-leavers searching for work for the first time.
"The number of unemployed increased in July with the start of the summer holidays. But the labour market is doing well overall," said Frank-Juergen Weise, president of the employment agency.
Carsten Brzeski, chief economist at ING-DiBa, said that "despite the small increase in non-seasonally adjusted terms, this labour market report is impressive... The labour market remains the showcase model of the strong German economy.
"Thanks to earlier reforms, ageing and immigration from crisis-battered eurozone countries, the German labour market has become solid as a rock and looks almost fully immune against any short-term volatility."
Brzeski pointed out that Germany had become the second-largest migration destination after the United States, and that this "is a blessing for the economy as it could slow down the negative impact from ageing."