The 35-year-old animal was pictured earlier this week with the names “Camille” and “Julien” etched onto their backs at La Palmyre Zoo in southwestern France.
Director Pierre Caille said visitors are allowed to touch the rhinos when the animals come close to the walls of their enclosure.
"A disrespectful person engraved names in the layer of dust and dead skin on the back of the rhinoceros," he added.
The zoo said it was “outraged by the stupidity and disrespect” shown but it would not be taking legal action against the two visitors.
Staff added that the rhino may not have noticed the visitors at the time.
The names "were quickly erased with the help of a brush and did not cause any discomfort to the animal,” the zoo said in a statement.
“Although the vast majority of our visitors show reservations and responsibility, unfortunately, there are always exceptions to confirm the rule,” it added. “At this point, we obviously remain attentive to the evolution of behaviour and reflect on the strengthening of our surveillance and security measures.”
When pictures of the rhino were shared widely on social media, some users were concerned that the animal appeared to be unusually thin.
Mr Caille admitted that this particular rhino was thinner than other animals but said this was due to their age and their health was not a matter of concern.
He added that the Zoo was considering installing CCTV in some parts of the park.
Nevertheless, Le Biome, a French wildlife protection charity, said the zoo "fell short of standards" by allowing visitors to touch the animals so easily.
Rhinos are rarely seen in the wild and three of the animal’s five species are critically endangered, largely due to the lucrative poaching trade.
La Palmyre Zoo has about 1,600 animals on its site and is visited by 750,000 people each year.
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