CPD Chief Buster Bingham said 21-year-old Barbara Jackson of Cleveland was found on her back in the kitchen with a stab wound.
Suspect Marvin Craft, 29, also of Cleveland, was arrested shortly after the incident for aggravated assault and domestic violence.
He is being held at the Bolivar County Regional Correctional Facility with no bond.
Bingham reported that the two had some form of relationship in the past and the stabbing was related to an argument.
According to John Paul Gates, manager of Pafford EMS service in Cleveland, Jackson was airlifted to the MED in Memphis.
The investigation is ongoing, and as of Thursday afternoon, Bingham said Jackson was in serious but stable condition.
Hospital officials confirmed this morning Jackson is at the MED but were unable to comment on her condition.
The Bolivar Commercial will have more as it develops