The film about a princess's mythical journey in ancient Polynesia took an estimated $81.1m (£65.3m) on its debut.
That makes it the second-highest Thanksgiving debut of all time, behind Disney's Frozen, which took $93.6m (£75.3m) on its release in 2013.
Some observers have said that Moana and its merchandise are appropriating Pacific Island culture.
Disney withdrew a children's costume promoting the film after activists branded it "brownface", or mocking of their culture by stereotyping.
The costume, a full-body suit with brown skin, traditional tattoos, grass skirt and bone necklace, represented the character Maui, considered a demi-god and ancestor by many Polynesians.
Disney said it regretted any offence.
JK Rowling's Fantastic Beasts and Where to Find Them fell to second on the US chart, taking $65.8m (£53m).
Gossip surrounding Brad Pitt's marriage break-up failed to spark a huge amount of interest in his World War Two romance Allied, which also stars Marion Cotillard.
It took $18m (£14.4m) over the long weekend, having cost $85m (£68.5m) to make, landing in fourth spot behind Doctor Strange.
Kyle Davies, Paramount's head of domestic distribution, said the film appealed to "older audiences" but noted those "don't storm the theatres [on] weekend one".
"I think they're going to take their time," he added.
Warren Beatty fared worse - his first film in 15 years, the 1950s Hollywood comedy Rules Don't Apply, took just $2.2m (£1.7m). The film is Beatty's first directed feature since 1998's Bulworth.
Bad Santa 2, released 13 years after the original and again starring Billy Bob Thornton, did a little better, taking $9m (£7.3m).
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Disney's latest animation Moana dominated the Thanksgiving box office over the five-day US holiday weekend.