The sepia-toned photo, posted Sunday on the royal couple's Instagram feed, shows the baby cradled in Harry's arms and clutching his father's finger.
The post is captioned: "Happy Father's Day! And wishing a very special first Father's Day to The Duke of Sussex."
The couple posted a picture of the baby's feet when Mother's Day was celebrated in the United States last month to mark Meghan's first as a mom.
The baby hadn't yet been born when the U.K. had its Mother's Day this year.
Archie Harrison Mountbatten-Windsor was born on May 6 and is seventh in line to the British throne.