The 43-year old Schumacher, who retired from the sport last month for the second time and after three years as a Mercedes driver, paid tribute to the Mercedes motorsport chief with a statement on his personal website.
"Since I entered professional motorsport, Mercedes and Norbert Haug together were part of it, so this step will mark a big break," said the German.
"We spent a lot of years together, being sporting combatants or allies, and Norbert has always been into this with full enthusiasm and wholeheartedly. He was living motorsports, and him leaving will tear a massive hole in both our sport and our team."
Mercedes announced on Thursday that Haug, 60, would stand down at the end of the month by mutual agreement after more than 20 years in the job.
Austrian triple champion Niki Lauda was named last October as the team's non-executive chairman and is expected to liaise between the factory and the Stuttgart-based carmaker, a job carried out by Haug until now.
Haug, who was instrumental in persuading Schumacher to come out of retirement in 2010, told Germany's SID news agency that he was leaving because of Mercedes's lack of results with their Formula One team.
"There is always somebody who has to accept overall responsibility," he said.
"Of course we have had our successes in the past three years but not consistently enough so a direction had to be set and a marker laid down."
Haug said Lauda's new role did not play a part in his departure.
Mercedes bought the championship-winning Brawn GP team at the end of 2009 and have won once with their renamed works outfit - this year's Chinese Grand Prix with Germany's Nico Rosberg.
Schumacher, winner of a record 91 races with Benetton and Ferrari, has had one podium finish in his three years with the team - a third in Valencia this season.
Mercedes have signed McLaren's Lewis Hamilton, the 2008 world champion, to replace Schumacher on a three-year contract from next year.