The news comes only weeks after the US ambassador to South Korea was stabbed and injured during a public event in Seoul.
Kennedy, the last surviving child of former US president John F Kennedy, took up her post in Tokyo in November 2013 as the first woman US ambassador to the Asian nation.
"We take any threats to US diplomats seriously. We take every step possible to protect our personnel," State Department spokeswoman Jen Psaki said in a statement, refusing to go into specific detail about the nature of the threat.
Japanese television station NTV reported earlier Monday that Japanese police were investigating death threats made by an anonymous caller against Kennedy.
A man speaking in English phoned the embassy "multiple times last month, saying he would kill Ambassador Kennedy," NTV television reported.
The caller had also threatened to kill the US consul general in Okinawa, Alfred Magleby.
The news came as First Lady Michelle Obama arrived in Japan on her first visit to the country, as part of a trip to highlight the importance of girls' education.
The US ambassador to Seoul, Mark Lippert, had to have 80 stitches to his face and was hospitalised for five days after he was stabbed earlier this month during a breakfast event in the South Korean capital.
Korean prosecutors are recommending that his attacker, a knife-wielding nationalist, face a charge of attempted murder for the "pre-meditated assault.
