Shah studied history at the University of Warwick and graduated in 1988. She joined the Radio 4 production team, moved from there to regional television news, and then to Today in 1991 as a producer. When The World Today launched on the World Service in 1999, Shah became one of its presenters.
In May 2013, she started a series of eight episodes in the BBC Radio 4 One to One series of interviews. As she belongs to a Jain family (the Jain religion is concerned with renunciation), the subjects of her interviews are people whose life has involved renunciation.