Wagner only joined Schalke in 2019 after three years with the Terriers.
"We had all hoped that we could improve on the pitch together with David Wagner," said Schalke sports director Jochen Schneider.
"Unfortunately, we haven't seen the right performances and results from the first two games for this to happen.
"We have therefore decided to make a fresh start. Despite the disappointing results, this wasn't an easy decision for us to make."