GM vice-chairman Steve Girsky will take over his duties on an interim basis while the firm searches for a replacement, the company said in a statement.
The chief executive of the parent company, Dan Akerson, paid tribute to the 56-year-old Stracke, saying he worked "tirelessly, under pressure, to stabilise this business."
Stracke said he believed "Opel/Vauxhall has a bright future" and said he was looking forward to taking on "special assignments" under Akerson.
In June, Opel's supervisory board approved a deep restructuring plan to steer the firm, a loss-making unit of US car giant General Motors, back into profit.
GM's European operations have run up billions of dollars in losses over the past 10 years.