The No. 5-seeded Tsonga will play No. 4 Andy Murray or No. 7 David Ferrer for a berth in the final.
Tsonga was the runner-up at the 2008 Australian Open, his only appearance in a major title match.
Against the 27th-seeded Kohlschreiber, who was making his Grand Slam quarterfinal debut, Tsonga hit 17 aces and served at up to 136 mph.
Tsonga broke serve three times, including twice in the final set.