Known affectionately by her husband and the wider public as "Loki", the popular chain-smoking Schmidt passed away overnight at her home in the northern city of Hamburg.
Her health had deteriorated since she broke a foot after a heavy fall at home.
The renowned botanist formed a powerful couple with her husband, whom she married in 1942. They were known for their exceptionally strong bond.
She published a series of books and campaigned for the protection of wildflowers in Germany. Since 1980, she has selected Germany's "flower of the year."
In a column entitled "Long live Helmut and Loki," mass circulation daily Bild wrote earlier this month that the two were "the best proof that even today, love can endure until death."
In a recent interview, she had said she and her husband had dreamed of celebrating their 70th wedding anniversary together in two years' time.
Helmut Schmidt, a centrist Social Democrat who led West Germany from 1974 to 1982, steered the country through Cold War tensions and a bloody wave of terror by far-left radicals that peaked in the autumn of 1977.