The 56-year-old Israeli was punished for remarks he made in a post-match interview about referee Mike Jones following West Ham's 2-1 defeat to Stoke City in the FA Cup quarter-final at the Britannia Stadium on March 13.
The ban, which takes place with immediate effect, means he will have to watch Saturday's match at Bolton Wanderers and the home game against Aston Villa at Upton Park on April 16 from the stands.
Grant was angry about the way Jones handled the second half of the match, especially awarding Stoke a penalty just 13 seconds after the break which Matthew Etherington missed.
West Ham have confirmed they are investigating claims that the families of their strikers Victor Obinna and Frederic Piquionne were racially abused by fans at Upton Park on Saturday.
The two came on as substitutes during West Ham's 4-2 defeat to Manchester United and the club said in a statement anyone found guilty of racial abuse "would be dealt with accordingly."
The statement on their website read: "The club takes such matters seriously and, with the police, is reviewing CCTV footage and gathering witness information. Anyone found responsible will be dealt with appropriately.
"This is an isolated incident and our supporters, like the club, are proud of our positive relationship with Kick It Out (the anti-racism campaign)."
