The seasonally adjusted jobless total fell by 11,000 to 2.695 million, the Labour Office said.
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The adjusted unemployment rate fell to 6.1 percent, its lowest level since German reunification in 1990. The rate had held at 6.2 percent for four consecutive months.
The eurozone jobless rate was down from 11 percent in April last year and the lowest figure for the 19 countries using the euro since August 2011, Eurostat said.
Across the 28 countries in the European Union, unemployment fell to 8.7 percent in April, down from 8.8 percent in March and 9.6 percent in the same month last year. That was the lowest rate for the EU since April 2009.
However, seven countries still have double-digit unemployment, with Italy at 11.7 percent, Spain at 20.1 percent and Greece at 24.4 percent.
The German economy expanded by 1.7 percent in 2015, its strongest rate in four years, mainly driven by robust private consumption and higher state spending on refugees.