Hamilton’s first Ferrari win in Barcelona closed the gap to 41 points behind Mercedes’ championship leader Kimi Antonelli.
The third major of the year starts on June 18 at Shinnecock Hills.
Captain not among 33-man group, but Ollie Chessum, George Martin and Charlie Ewels added.
The Yorkshireman will lead England at The Oval this week, having stepped away from the role in 2022.
Winner number 97 for Aidan O’Brien at Royal Ascot.