The clip posted by Trump's daughter Ivanka shows 5-year-old Arabella Kushner singing best wishes for the holiday while playing with a traditional Chinese puppet.
On Wednesday, Ivanka and Arabella made a surprise visit to the Chinese Embassy in Washington to take part in the festivities.
While the Trump women received praise, the lack of a greeting from the president "triggered heated discussion" among the Chinese public over the possible ramifications for bilateral relations, the official newspaper Global Times said Friday.