Fanny Mendelssohn was born in Hamburg, Germany, the eldest of four children born to a prominent banker in Hamburg, Abraham  and the granddaughter of the notable philosopher, Moses Mendelssohn.

Fanny was given the same education and scholarly opportunities as her brother, Felix Mendelssohn. Fanny as well was a child prodigy and composed music.  The Mendelssohn home was a center of intellect, and Fanny's parents strove to give their children the best education possible. The Mendelssohn's were friends with some of the greatest intellects of their day.

Unfortunately, Fanny ultimately was forced to adhere to the attitudes towards women at that time, in that they could not have a career but must marry and be good wives. Apparently Fanny's father was merely tolerant of her compositions, which numbered about 466, many published under Felix's name. It is due to her close relationship with her brother, Felix, that we know of these compositions at all!

In a letter written to Fanny by her father:

                          "You must still improve. You must become still more steady and collected,
                           and prepare more earnestly and eagerly for your real calling, the only 
                           calling of a woman,—I mean the state of a housewife. Women have a
                          difficult  task; the constant occupation with apparent trifles, the
                           interception of each drop of rain, that it may not evaporate, but be
                           conducted into the right channel, the unremitting attention to every detail,—
                           all these are the weighty duties of a woman."

Fanny Mendelssohn married Wilhelm Hensel in 1829, a man who was supportive of her compositions. Fanny's only known public performance was in 1838 when she played Felix's Piano Concerto No. 1.

Hensel died in 1847 from complications from a stroke. Felix died only 6 months later.

Sources:
Rowlands, Walter.  Among the Great Masters of Music.  London: E. Grant Richards, 1906.