An official told BBC that the Israeli police had launched an investigation but initial findings suggested no foul play.
Mr Du, 57, was only appointed ambassador in February having previously served as envoy to Ukraine.
The ambassador was married and had a son but his family had still to join him in Israel.
He was living in the Tel Aviv suburb of Herzliya.
An Israeli police spokesman told Reuters news agency: “As part of the regular procedure, police units are at the scene.”
Israel’s Channel 12 TV, quoting unnamed medical sources, said initial indications were that Mr Du had died in his sleep of natural causes.
In a message published on the embassy’s website just after his appointment as ambassador, Mr Du praised the relations between “the second largest economy in the world and Israel the start-up nation” .