Markle and Prince Harry, who live in Montecito, California, had travelled to Jackson Hole for a weekend with friends.
Photos shared by a fan show Meghan dressed casually in black jeans, a white top and fedora hat, while attending to Archie, who turned three on May 6.
Archie had on a baseball cap in the American flag colours and he held an American flag.
Prince Harry was also pictured standing close to his family. 1-year-old Lilibet was nowhere in sight.