Suchet was born in London, the son of Joan (née Jarche), an actress, and Jack Suchet, a doctor. Suchet's father was Jewish and his mother was an Anglican; Suchet was raised in the Anglican religion. His paternal grandfather lived in Latvia. His surname was shortened from Suchedowitz to Suchet. He also has some French blood on his mother's side.[citation needed]

After attending the Wellington School in Somerset, he took an interest in acting and joined the National Youth Theatre at eighteen. He studied at the London Academy of Music and Dramatic Art, where he now serves as a council member. He began his acting career at the Watermill Theatre, Bagnor, Berkshire, and retains a great affection for the place, saying that it "fulfils my vision of a perfect theatre".