While there is no standard term for a baby monkey, it is usually referred to as an infant. Baby monkeys are helpless when they are born. In most species of monkey, the mother takes on the parenting duties when the infant is young.
Marmosets and tamarins are usually born in multiples, but the mothers don't bear the brunt of responsibility for raising the youngsters. Unlike other species, the father takes the lead role with the mother only feeding the infants. The pygmy marmoset is the smallest of the monkey species and weighs around 4 ounces when it is an adult.