The Blues striker was handed the ban at an FA Disciplinary hearing on Friday afternoon where he admitted to a charge of improper conduct following his sending off against Arsenal last weekend. He had failed to leave the field promptly and approached the match officials in an aggressive manner.
Heskey, who has already served an automatic one game ban for the red-card picked up against the Gunners, was also fined £5,000 for his actions.
He will now miss the live television game against The Hammers at Upton Park on Monday night but will be available for selection when Blues visit Stoke for their FA Cup 5th Round tie next Sunday.