The American's decision marks the second straight year that he has opted not to play in the tournament.
Stricker began reducing his playing schedule last year in order to spend more time with his family, and has once again opted to forego his place in the event at Royal Liverpool.
His withdrawal gives Japan's Ishikawa the chance to compete for the famous claret jug.
The 22-year-old claimed his first victory since 2012 by winning the Nagashima Shigeo Invitational Sega Sammy Cup last weekend.
That triumph moved him up to number 76 in the world and made him first reserve for The Open, which starts a week on Thursday, as a result.