BBC NewsThe US Embassy in Tokyo reportedly received the threatening phone calls last month from an English speaker.
US Consul General Alfred Magleby, who is based on the island of Okinawa, was also a target of the threats.
Ms Kennedy is the daughter of former US President John F. Kennedy, and became the US ambassador to Japan in November 2013.
Japanese media reports said the phone calls came last month and the caller spoke English.
The caller’s motive is not known.
Police in Tokyo and the embassy are refusing to comment.
A police official in Okinawa speaking anonymously to the Associated Press news agency confirmed the investigation that was also being reported on by the Yomiuri Shimbun newspaper.
Ms Kennedy became ambassador to Japan in November 2013Mr Magleby is stationed on the southern island of Okinawa, where approximately 25,000 US troops are based.
Reports of the calls surfaced as US First Lady Michelle Obama begins a multiday trip to Japan. She will also visit Cambodia.
Earlier this month, US Ambassador to South Korea Mark Lippert was attacked by a man with a knife and was hospitalised for several days.
Last month? And the BBC is just now reporting it? What happened to those amazing powers of prognostication they had when they reported building seven falling 20 minutes before it did? Oh wait, Osama Bin Laden was in charge of the BBC back then. And NORAD also, apparently. Never mind.
I guess they don’t have caller id over there in Japan.
below is a comment Millard tried to send in, was blocked. Said he will be back after he redoes his computer.
“yes Coraline lets not be looking into tpp, and fukushima.”
Thank you Paul for the post. After not 1, but 2 system restores and a hard line installation, I’m back!
Hey Millard good to see your up. 😎
They were probably waiting for the right time to use this death threat card. You know timing is everything with these bastards.