Some 42,300 unaccompanied minors entered Germany from abroad last year, the country's Federal Office for Statistics said.
This was an increase of 30,700, or 263%, compared with the previous year, the office said in a statement.
About 91%, or some 38,700, of these children and teenagers were male, while only about 3,600 girls entered Germany without their parents.
Germany saw an unprecedented influx of migrants in 2015.
More than one million people registered for asylum, the majority of them from Syria, Afghanistan and Iraq.
Unaccompanied refugee children are normally taken into care by the country's youth welfare offices.