Family spokesman Reinhard Poetschke told the dpa news agency today that the German Foreign Ministry said in a letter that Johannes, Sabine and Simon Hentschel were dead.
He says it appears the parents were killed while the boy, an infant at the time of kidnapping, died of an infection.
The Hentschels, who were working for a small Christian aid organisation, were kidnapped with their three children in northern Yemen in 2009.
Their two daughters, Lydia, 10 and Anna, 8, were freed in 2010 with Saudi Arabia's help and today live with relatives in Germany.