Tokyo police are looking into calls to the US Embassy threatening Kennedy and similar ones targeting Alfred Magleby, the US consul general on the southern island of Okinawa, an Okinawa police official said on condition of anonymity because he was not authorised to comment on an investigation by Tokyo authorities.
Tokyo police declined to comment. State Department spokeswoman Jen Psaki said the US government takes threats to American diplomats seriously.
"We are working with the Japanese government to ensure the necessary measures are in place. We will not comment on the specific details of any threats or the steps we take to address them," she said.
Kennedy has drawn much attention since arriving in Japan in November 2013 because of being the daughter of former President John F Kennedy.
She has made well-publicised visits to the Fukushima nuclear plant devastated by a 2011 earthquake and tsunami, and to the annual commemorations of the US atomic bombings of the cities of Hiroshima and Nagasaki.
Okinawa is home to about half of the 50,000 American troops based in Japan, and residents have frequently complained about crime, noise and other issues related to the US bases.