Because he is either a bonobo or a Barbary macaque, Curious George the monkey most likely lacks a tail. His inventors, H.A. and Margret Reys, are both gone, and they never answered this important query.
A prehensile tail is usually always present on monkeys, whereas it is never present on apes. Because of this, it makes sense that informed readers of the story would be perplexed by his diminutive size.
When Curious George was made in the 1930s, lesser apes and even chimpanzees were sometimes referred to as monkeys. Despite being erroneous taxonomically, this usage was accepted at the time. George may thus be the bonobo, or diminutive chimpanzee, that he most resembles.
He could be a Barbary macaque as well. African monkeys are called macaques, however this particular variety lacks a tail. George is most likely a bonobo who has been misidentified as a monkey because he does not resemble a Barbary macaque.