The Missouri State Highway Patrol says the crash happened around 1:30 p.m., about a mile north of Corning.
According to the Patrol, a northbound semi driven by a 50-year-old woman from Galloway, Ohio struck the towed unit of a semi-tractor trailer that was stopped on the east shoulder of the interstate.
The woman's truck crossed the roadway and came to rest upright in the median. The parked semi ended up upright in the east ditch. Both trucks caught fire and were totaled.
The driver of the parked rig, a 64-year-old man from Louisiana, and the Ohio woman were taken by Atchison-Holt Ambulance to Mosaic Life Care in St. Joseph with injuries.
