Handling large numbers exceeding 15 digits in Perl can be effectively managed using the Math::BigInt module, which supports arbitrary size integer math. For numbers with 10,000 digits or more, Math::BigInt is suitable as it allows for calculations without losing precision. Users can refer to the official documentation for detailed guidance on implementing this module in their Perl scripts. The discussion emphasizes the importance of utilizing Math::BigInt for operations involving extremely large integers to ensure accurate results.