McKidd was born on 9 August 1973, in Elgin, Moray, Scotland, the son of Kathleen, a secretary, and Neil McKidd, a plumber. He grew up in a council estate near Inverness. At 17, McKidd worked at the Macallan distillery in Speyside. He later went to work with the Lumsden family of coppersmiths. He attended Seafield Primary School and Elgin Academy. and was a member of the local amateur dramatic group, Moray Youth Theatre. Planning to study engineering, he initially attended the University of Edinburgh, then decided to enroll at Edinburgh's Queen Margaret College to study drama. He joined Edinburgh University's student theatre company, Bedlam Theatre, where he was a member of the improvisational comedy troupe The Improverts.