The Israeli will pick and prepare the side as usual, but will not be on the bench at the Britannia Stadium as he is required to participate in 25 hours of fasting and prayer over the course of Friday and Saturday.
His coaching staff will oversee first-team affairs for the bottom-of-the-table encounter.
A statement on club website www.whufc.com read: "Avram Grant will not be taking the team for the match against Stoke City on Saturday.
"Out of respect for the traditions, heritage and religious obligations of the Jewish holy day of Yom Kippur, Avram Grant will not be in the dug-out at Stoke City this Saturday.
"Dating back thousands of years, Yom Kippur - or Day of Atonement - is the most significant day of the year. It is a strict day of fasting and abstaining that forbids all followers to work.
"West Ham United fully respect and understand the situation. It is very unusual for the day to clash with the fixture list.
"The manager will pick and prepare the side as usual and fully ensure that all are ready for the match this weekend.
"Assistant manager Zeljko Petrovic, senior coach Paul Groves and first-team coach Kevin Keen will all be on the bench at the Britannia Stadium."