The Yasukuni Shrine in central Tokyo is dedicated to 2.5 million war dead, mostly Japanese, who perished in conflicts since the late 19th century.
That number includes senior military and political figures convicted by an international tribunal of war crimes prior to and during World War II.
A Japanese prime minister has not visited the shrine since 2013, but Takaichi's predecessors Shigeru Ishiba and Fumio Kishida regularly sent offerings for the biannual spring and autumn festivals.
Dozens of lawmakers pay their respects every year during the festivals and in August for the anniversary of the emperor announcing Japan's surrender in 1945.
Former prime minister Shinzo Abe visited the shrine in 2013, sparking fury in Beijing and Seoul and earning a rare diplomatic rebuke from close ally the United States.
Takaichi sent a "masakaki" tree offering, the source told AFP, while public broadcaster NHK and Jiji Press also reported that she sent the offering.
China reacted angrily, calling the shrine a "spiritual instrument and symbol of the wars of aggression launched by Japanese militarism."
"China firmly opposes and strongly condemns the negative moves by Japan regarding the Yasukuni Shrine, and has made solemn representations and a strong protest to the Japanese side," foreign ministry spokesman Guo Jiakun said.
South Korea expressed "deep disappointment and regret" on Tuesday over the offering.
"Our government urges Japan's responsible leaders to face history squarely and to demonstrate, through action, a humble reflection on and a sincere remorse for its past," foreign ministry spokesman Park Il told reporters.
"We reiterate that this serves as an important foundation for building a future?oriented South Korea-Japan relationship grounded in mutual trust," he said.
Japan's top government spokesman Minoru Kihara declined to comment on the reports.
Takaichi visited the shrine in August last year, before she became prime minister, and told local media: "Honouring the spirits of those who devoted their lives for their country is something each individual should do in accordance with their own conscience."