Knappett was born in Bradford, West Yorkshire and grew up in Bingley before studying at the University of Manchester. She was a founder member of Lady Garden, a sketch group who met in Manchester in 2005 and performed their first show at the 2008 Edinburgh Fringe Festival, returning in 2009 and 2010. During this period, the group toured throughout England, and performed at Sheffield, Manchester, Brighton, Comedy Festivals in 2008, were 2009 Hackney New Act & Laughing Horse Finalists, and won an Argus Angel for their show in the Brighton Fringe in May 2009.
Knappett was the creator, writer, executive producer and star of comedy Drifters for E4 in which she played the role of Meg.  Due to the popularity and success of the first series, it was quickly repeated on Channel 4 and later commissioned for a further three. Knappett was nominated for an RTS award for Best Comedy writer and Broadcast award for Drifters series 2. Series 4 aired on E4 and Channel 4 at the end of 2016.
Knappett played the lead role of Lisa in The Inbetweeners Movie and appeared in Steve Coogan's Alan Partridge Movie Alpha Papa and the TV Movie Irreversible alongside David Schwimmer. Other credits include Drunk History for Comedy Central, Mid-Morning Matters for Sky One, Twenty Twelve for BBC Two, E4's Meet the Parents for Objective Productions, How Not to Live Your Life and Lunch Monkeys for BBC3. She also played the role of Carly in the BBC Radio 4 comedy series Shedtown alongside Johnny Vegas. She has also recorded a string of pilots, including Everything Happens for No Reason written by Richard Herring, alongside Noel Fielding 
Her brother is the comedy producer Ben Knappett.
She has in interviews mentioned that Drifters was a semi-autobiographical, therapeutic re-writing of history.
- Hannah Begbie. "Jessica Knappett CV". United Artists. Retrieved 26 August 2011.
- Harriet Gibsone (10 October 2016). "Drifters' Jessica Knappett on turning her wilderness years into a TV smash". The Guardian.
- Stuart Husband; Horatia Harrod (27 October 2010). "Britain's Funniest Women". The Telegraph. Retrieved 26 August 2011.
- Jessica Knappett (26 March 2017). "The Guardian - Life and Style - How I married a world-champion air guitarist who turned up on my doorstep". The Guardian.
- Jessica Knappett (16 April 2017). "The Guardian - Life and Style - Nothing prepared me for pregnancy, apart from the never-ending hangover of my 20s". The Guardian.