Suchet's father was of Lithuanian-Jewish descent, the son of Izidor Suchedowitz, originally from Kretinga in the Pale of Settlement of the Russian Empire. At some point, the family name was recorded as "Schohet", a Yiddish (from Hebrew shochet) word defining the profession of kosher butcher. Suchet's father changed his surname to Suchet while living in South Africa. David's mother was born in England and was Anglican (she was of Russian-Jewish descent on her father's side, and English Anglican on her mother's side). He was raised without religion, but became a practising Anglican in 1986, and was confirmed in 2006.
Raised without religion, in 1986 Suchet underwent a religious conversion after reading Romans 8 in his hotel room; soon afterwards, he was baptised into the Church of England. Suchet stated in an interview with Strand Magazine, "I'm a Christian by faith. I like to think it sees me through a great deal of my life. I very much believe in the principles of Christianity and the principles of most religions, actually—that one has to abandon oneself to a higher good." In 2012, Suchet made a documentary for the BBC on his personal hero, Saint Paul, to discover what he was like as a man by charting his evangelistic journey around the Mediterranean. Two years later, he would film another documentary, this time on the apostle Saint Peter.