The 46-year-old woman died when the construction crane smashed through the roof above the checkout area of the Aldi supermarket in Bad Homburg.
Around 47 people were in the supermarket at the time -- 40 customers and seven staff.
The cause of the accident was not yet clear.
The crane driver was seriously injured and flown to hospital. Police said they did not expect the number of fatalities to rise.
Aldi in a statement extended its condolences and sympathy to the victims.