Solemani was born in the London Borough of Camden and grew up in Crouch End. Her father is a Persian Jewish mathematics lecturer (now retired). Her mother, who died of cancer when she was 16, was a sociology teacher of Northern Irish descent.
After passing her A levels at the Henrietta Barnett School, she took a gap year before reading Social and Political Sciences (now the Human, Social and Political Sciences Tripos) at New Hall, Cambridge and graduating with an MA (Hons).
At Cambridge, she joined the Cambridge University Footlights Dramatic Club and became social secretary during her first year, replacing Dan Stevens, and then vice president. She went down in Footlights history for writing the biggest all-female comedy sketch ever performed on a Footlights stage, writing twenty five female students into her sketch 'Brawl'.
Solemani was a member of the National Youth Theatre during her gap year, starring as Elaine in the West End theatre production of The Graduate and as 'Ayesha' in the critically acclaimed National Theatre production of Sanctuary.
Solemani was a member of the Young Writer's Group attached to the Royal Court Theatre, and a writer at the Young Vic Theatre. Two plays she wrote were produced at Soho Theatre. Another of her works, The Cost of Things (2010), was presented at the Public Theater New York under the aegis of the Old Vic Theatre as part of the TS Eliot Project.
In 2011, she wrote The Baron which received the Old Vic New Voices 'Ignite' award.
In 2009, she appeared in Simon Stephens 'Pornography' at the Tricycle Theatre London and in 2012, she appeared as 'Maryam' in the play The House of Bernarda Alba at the Almeida Theatre. She wrote Up the Royal Borough, part of an evening of plays in response to Owen Jones' Chavs at the Lyric Hammersmith; it was performed to good reviews.
Solemani's first film role was as a tableaux girl in Mrs Henderson Presents, which she performed during her third year of college.
Her first major TV role was as "Becky" in BBC Three sitcom Him & Her, which was first broadcast in November 2010, and ran for four series ending in 2013.
In 2012, Solemani starred in the BBC Three comedy, Bad Education, including its spin off movie The Bad Education Movie.
In 2013, Sarah starred in the BBC and Hulu's The Wrong Mans alongside James Corden. She went on to reprise the role in the second series.
Solemani wrote and starred in an episode titled Aphrodite Fry in the Sky TV series Love Matters that aired in 2013. In 2014, she wrote the television film The Secrets on BBC One at 9pm to critical praise.
Currently in Hollywood, Sarah was chosen by Bill Hader and Alec Berg to be part of their writing team on Hader's new HBO show Barry.
Solemani has contributed to the New Statesman, The Guardian, The Independent and Harper's Bazaar.
She writes regularly for the publications Red and Glamour.
Solemani was awarded third place in the Barry Amiel and Norman Melburn Trust/New Statesman Prize for New Political Writing on the subject: "Do women's rights remain the privilege of the developed world?" in 2005.
In 2011, Solemani won the Royal Television Society award for best Comedy Performance for her role in Him & Her along with her co-star Russell Tovey.
In 2012, Solemani was named one of the year's Broadcast Hot Shots.
Sarah is against the criminalisation of sex work, and has been a champion for sex worker rights since 2002. She was nominated by the English Collective of Prostitutes (ECP) to represent them in Parliament in order to halt further efforts to criminalise clients. She was a vocal supporter of former shadow Home Secretary Yvette Cooper in the 2015 Labour Leadership race. She has introduced Cooper at various Labour Party events and has contributed to her speeches.
Solemani married Daniel E. Ingram , a sustainable investment expert specialising in climate change in Petah Tikva, Israel on 3 June 2012. Their daughter was born in December 2013.
The couple revealed their daughter's Godparents at a ceremony in the New London Synagogue. Their child's Godfather is comedian Simon Amstell and Godmother is Dr Orlanda Ward, a gender and politics expert and teaching fellow at University College London.