At least, he doesn't have the characteristics of any known species of monkeys. The fact that he doesn't have a tail would indicate that he is an ape, not a monkey. There are tailless monkeys (the Barbary Macaque and the Celebes Crested Macaque) but they look NOTHING like Curious George.
In fact, parents in a school in Atlanta were so bothered by the inaccuracies of George's anatomy that they tried to have Curious George books removed from a school. (More about this and other Curious George controversies here). Ultimately, the parents did not pursue removing the books. However, this begs the question: why is he called a monkey if he has no tail?
At the time Curious George was written, most people referred to both monkeys and chimpanzees as monkeys. Today, we are more careful to make the distinction between the two animals.