One of the Americans arrested was dressed in a costume and allegedly climbed into the monkey's habitat at the Ichikawa City Zoo on Sunday, according to NHK.
Another man who was filming the stunt was also arrested.
Both are said to be U.S. nationals in their 20s.
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There is no video yet of the incident.
This comes as the New York Times reports that starting Tuesday, the zoo will restrict the viewing area at the enclosure housing Punch, and will install "intrusion prevention nets" and institute "permanent patrols."
Punch went viral earlier this year after carrying around a stuffed monkey as he struggled to fit in after being abandoned.