The top-seeded Frenchman was made to sweat before claiming a 4-6 6-3 6-4 win in two hours nine minutes.
Kamke saved eight break points in the opening set, taking the only one that came his way, but the home favourite was far more ruthless in the second and third.
One break in each was enough to set up a last-four meeting with another German, Florian Mayer.
Mayer, the eighth seed, also had to come from behind to win his quarter-final against Argentinian Carlos Berlocq.
He won 5-7 6-4 7-5.
Giles Simon, the second seed, and Nicolas Mahut ensured there would be three Frenchmen in the last four.
Simon beat sixth-seeded American Sam Querrey 6-4 7-6 (7/1), while Mahut saw off Germany's Benjamin Becker 6-2 6-4.