Kensington Palace announced the gift on Saturday, saying the giant tooth was given to the seven-year-old prince when Attenborough attended a private viewing of his latest environmental documentary with members of the Royal Family.
Attenborough found the fossil during a family vacation to Malta in the late 1960s, the palace said. It was embedded in soft yellow limestone, and is believed to be about 23 million years old.
However, Maltese Culture Minister Jose Herrera said the tooth should be in a local museum and promised to "set the ball rolling" to get it back.
"There are some artifacts that are important to Maltese natural heritage and which ended up abroad and deserve to be retrieved," Herrera told the Times of Malta, without giving details of how he intended to recover the fossil.
The tooth once belonged to a megalodon, an extinct species of giant shark that could grow up to 16 meters (52 feet).