It happened Friday afternoon at 3:10pm at West McCord Street and North High Street.
Witnesses report the bicycle driven by a 47-year-old Neosho man was heading northbound and failed to stop at the intersection.
The bike collided with a US Postal Service vehicle that was traveling eastbound on McCord.
The man on the bike has severe injuries and was immediately taken to a nearby hospital.
Anyone who has any additional information should contact the Neosho Police Department at 417-451-8333.