Cobblers boss Ian Sampson launched an appeal after Osman was dismissed in the 1-1 draw at Port Vale on Saturday.
But the FA rejected his appeal at a hearing so Osman will begin his ban against Morecambe on Tuesday evening.
Osman was also sent off against Vale earlier this season but had that card overturned.
He will also miss games against Aldershot and Hereford, but will be available for the trip to Southend.
Source: PA
Source: PA