The primates were monitored in three situations: while they were secure at home with their cage-mates, while they were alone and while they were exposed to an unfamiliar human carer.
They found that in the most anxious monkeys, there was increased activity within the amygdala, the part of the brain which deals with fear and aggression.
This was true even when the monkeys were placed in a non-stressful environment.
18-months later, tests were carried out once again, and it was found that the now adult monkeys were still anxious.
The scientists say their findings could have implications for the treatment of mental illness, reports The Independent.
"Prior to this research, we didn't know that you could detect a tendency towards anxiety so early in life, or that this level would remain so constant," lead author Dr Ned Kalin told the paper.
"Looking at a way to settle down that part of the brain could be a major factor in reducing anxiety for many people," added Dr Kalin.
The study is published in the online journal Public Library of Science.