Officials said parents must submit a scanned copy of their child's birth certificate within 60 days of the birth to claim one of the 2,013 silver pennies.
The Royal Mint said silver is a traditional good luck gift for new parents.
"The birth of the royal baby will be a joyous occasion not just for Their Royal Highnesses The Duke and Duchess of Cambridge but also for the whole nation," said Shane Bissett, director of commemorative coin at the Royal Mint. "However, it will also be a special day for many mothers and fathers across the country as they too welcome the arrival of their new baby, hence why we wanted to extend this historical moment to them with a lucky silver penny."
The royal baby will be third in line for the British throne after Prince Charles and Prince William. William and Kate said they have decided not to know the baby's gender before the birth.