She received her first piano instruction from her mother, who had been trained in the Berliner-Bach tradition by Johann Kirnberger, who was himself a student of Johann Sebastian Bach. Thus as a 13 year old, Fanny could already play all 24 Preludes from Bach's The Well-Tempered Clavier by heart, and she did so in honor of her father's birthday in 1818. She studied briefly with the Pianist Marie Bigot in Paris, and finally with Ludwig Berger. In 1820 Fanny, along with her brother Felix, joined the Sing-Akademie zu Berlin which was led by Carl Friedrich Zelter. Zelter at one point favored Fanny over Felix: he wrote to Johann Wolfgang von Goethe in 1816, in a letter introducing Abraham Mendelssohn to the poet, 'He has adorable children and his oldest daughter could give you something of Sebastian Bach. This child is really something special'. Much later, in an 1831 letter to Goethe, Zelter described Fanny's skill as a Pianist with the highest praise for a woman at the time: "She plays like a man." Both Fanny and Felix received instruction in composition with Zelter starting in 1819.

However, Fanny was limited by prevailing attitudes of the time toward women, attitudes apparently shared by her father, who was tolerant, rather than supportive, of her activities as a Composer. Her father wrote to her in 1820 "Music will perhaps become his [i.e. Felix's] profession, while for you it can and must be only an ornament". Although Felix was privately broadly supportive of her as a Composer and a performer, he was cautious (professedly for family reasons) of her publishing her works under her own name. He wrote:

In 1829, after a courtship of several years, Fanny married the Painter Wilhelm Hensel and the following year she had her only child, Sebastian Ludwig Felix Hensel. Her husband was supportive of her composing. Subsequently, her works were often played alongside her brother's at the family home in Berlin in a Sunday concert series (Sonntagskonzerte), which was originally organised by Fanny's father, and after 1831 carried on by Fanny herself. Her public debut at the piano (and only known public performance) came in 1838, when she played her brother's Piano Concerto No. 1. In 1846, she decided, without consulting Felix, to publish a collection of her songs (as her Op. 1).

In turn Fanny helped Felix by constructive criticism of pieces and projects, which he always considered very carefully. Their correspondence of 1840/41 reveals that they were both outlining scenarios for an opera on the subject of the Nibelungenlied: Fanny wrote 'The hunt with Siegfried's death provides a splendid finale to the second act'.

The siblings shared a great passion for music. Felix did arrange with Fanny for some of her songs to be published under his name, three in his Op. 8 collection, and three more in his Op. 9. In 1842 this resulted in an embarrassing moment when Queen Victoria, receiving Felix at Buckingham Palace, expressed her intention of singing the Composer her favourite of his songs, "Italien" (to words by Franz Grillparzer), which Mendelssohn confessed was by Fanny.

Fanny Hensel died in Berlin in 1847 of complications from a stroke suffered while rehearsing one of her brother's oratorios, The First Walpurgis Night. Felix himself died less than six months later from the same cause (which was also responsible for the deaths of both of their parents and of their grandfather Moses), but not before completing his String Quartet No. 6 in F minor, written in memory of his sister.

Amongst her works is the Easter Sonata written in 1828, which was unpublished in her lifetime, then discovered and attributed to her brother in 1970, before examination of the manuscript and a mention of the work in her diary finally established that the work was hers in 2010. It was debuted in her name on 8 March, 2017, International Women's Day.

In recent years, her music has become better known thanks to concert performances and a number of CDs being released on labels such as Hyperion and CPO. Her reputation has also been advanced by those researching female musical creativity, of which she is one of the relatively few well-documented exemplars in the early 19th century.