Kenny was born in the North London Borough of Haringey and she attended North London Collegiate School (NLCS) in Edgware, Middlesex, London, until 2008. She is of Welsh and Irish heritage.

In 2010 Kenny was painted by Rolf Harris as Titania from Shakespeare's A Midsummer Night's Dream for an edition of BBC TV's Arena ("Rolf Harris Paints His Dream").

In 2011 she was cast as Danielle Reeves in the BBC Three dramedy Pramface alongside her Beaver Falls co-star Scarlett Alice Johnson. Pramface piloted in late February 2012 and was met with good reception, so much so the second series was commissioned by the BBC before the first series had even aired. She reprised her role for the second series which began airing in the new year of 2013 and was broadcast a second time on BBC One throughout the summer of 2013. She reprised her role again for a third series which commenced airing in late February 2014.

She joined the cast of E4's Beaver Falls for its second series playing the character Hope. The second series began airing in early August 2012 with the final episode of the series airing in early September 2012. It was announced on 22 September 2012 that the drama would not be recommissioned.

She played the role of Rachel alongside Matthew Crosby, Ben Clark and Tom Parry in the first series of BBC Three's sitcom Badults which aired in the summer of 2013. A second series was commissioned but it was announced that Kenny would not feature in it.

In 2016 Emer Kenny worked as a scriptwriter on Irish soap Red Rock for a few episodes.

In 2017 she joined the cast of the BBC TV series Father Brown as Bunty Windermere, the wayward niece of Lady Felicia.