German green group Deutsche Umwelthilfe confirmed to Reuters that it filed the legal action on Monday (September 20) evening.
It's the first time that German citizens have sued private firms for exacerbating climate change.
Other activists including Greenpeace plan a similar case against Volkswagen.
The moves come after Germany's top court last year ruled that the country's climate law was not doing enough to protect future generations, and set carbon emissions budgets for major sectors.
Now the case demands that the firms set a 2030 date for phasing out combustion-engined vehicles, and take steps to limit their emissions before then.
Both have so far avoided committing to an end date for traditional cars.
BMW and Daimler confirmed to Reuters that they have not accepted the demands, though Daimler does aim to produce only EVs by 2030
BMW wants half its sales to be electric by then.
If the two firms lose, more cases are expected against other companies such as airlines and energy providers.
Oil giant Shell has already lost a similar case in the Netherlands.