[1][3] Although they have been observed in the wild in Puerto Rico, they are probably the result of escaped pets, and no reproduction has been recorded.

[4] The Cuban amazon was formally described in 1758 by the Swedish naturalist Carl Linnaeus in the tenth edition of his Systema Naturae.

[5] Linnaeus cited the description and illustration of the "white-headed parrot" in George Edwards' A Natural History of Uncommon Birds which was published in 1751.

[6] Linnaeus gave the type locality as "America" but this was restricted to eastern Cuba by Thomas Barbour in 1923.

[7][8] The Cuban amazon is now one of around thirty species placed in the genus Amazona that was introduced by the French naturalist René Lesson in 1830.

[11] Traditionally, most authorities have recognized four subspecies of the Cuban amazon,[12][13][10] thereby following the 1928 review by James Lee Peters.

[16][17][18] A recent review based on morphology and plumage supported the distinction of A. l. palmarum (at least if restricted to the population on Isla de la Juventud), it having a longer wing chord and metatarsus, and a larger rosy pink throat patch than A. l. leucocephala of the Cuban mainland.

[26] The Cuban amazon was seldom-seen in aviculture outside of Cuba and Florida (where it was bred in captivity by Cuban immigrants) until the 1980s, and is considered one of the more difficult to breed amazon parrots, with aggressive behaviour from cock birds towards their mates and their own chicks a relatively common occurrence.

In 2020, the authorities held an amnesty during which parrot owners could legally register their pets, which were then given health checks and fitted with microchips and leg bands in order to identify and distinguish them from wild birds.