The 55-year-old Kennedy's arrival comes a week before the 50th anniversary of her father's assassination in Dallas.
"Hajime-mashite ('Nice to meet you')," a smiling Kennedy told reporters in Japanese at Narita airport before moving to the US embassy in downtown Tokyo.
"It is a special honour for me to be able to work to strengthen the close ties between our two great countries... Our alliance is critical to a prosperous and peaceful world," she added in a brief speech, accompanied by her husband, Edwin Schlossberg.
Kennedy is the first female US ambassador to the Asian giant, which consistently ranks lower than other wealthy nations on women's empowerment in politics and business.
Kennedy's appointment has been hailed in Japan, although some critics have voiced concern at having a diplomatic novice in the important post at a time of high tensions between the close US ally and a rising China.
A scion of political royalty, Kennedy has largely shunned the limelight though she has publicly championed her family's brand of progressive politics.
She played a pivotal role in the Democratic Party's primary in 2008 where she was an early and vocal backer of Barack Obama against perceived front-runner Hillary Clinton.