Speaking to reporters, Kennedy described the ceremony as "wonderful."
"I am honored to serve my country," she said.
The procession was accompanied by palace officials in European-style ceremonial costumes, including a footman in breeches. Her carriage, the spokes of its coppery wheels gleaming in the late afternoon sunshine, was led by a horseman astride a white horse.
Kennedy was appointed ambassador after helping President Barack Obama's re-election campaign.
She is the first woman to be U.S. ambassador to Japan, the United States' fourth-largest trading partner and home to the Navy's 7th Fleet and 50,000 American troops.
She is to meet with Prime Minister Shinzo Abe later this week and visit Yokota Air base, an American military facility west of Tokyo. Friday is the 50th anniversary of her father's assassination.
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Online: twitter.com/CarolineKennedy