Former world No. 1 Murray returned to action following a seven-month injury layoff at the charity event organised by his brother Jamie this week.
Ward will take Murray’s place in the match against Norrie.
On Saturday, Murray warned that the ATP’s revised calendar is not safe for players, who will be forced to skip major events due to the crammed schedule.
He also suggested he will skip the tournament in Cincinnati to get his preparations for the U.S. Open in order.