"Of course, you can't wish for more than winning twice in two races and I'm obviously delighted," said Schumacher Jnr.
Schumacher Jnr's success behind the wheel comes as his father, a seven-time world F1 champion, continues his rehabilitation at home from head injuries suffered in a skiing accident in December 2013.
"The speed was there, the car was good, everything is okay," the teenager told broadcaster Sport1 at the Lausitzring, near Dresden.
After claiming victory in the early afternoon's first race following a mass pile-up involving 11 cars on the first lap, Schumacher managed a second victory in the evening race.
More From This Section
Schumacher will be bidding for a hat-trick on Sunday in the final of the three races.
The German now has three wins in German F4 this season having picked up a victory on the opening weekend in April.
He has also racked up three victories from six races in Italian F4 this season, which runs parallel to the German championships, and is also second in their drivers' championship.