The Houston Police Department said its Westside Division officers were called to the 9900 block of Richmond Avenue, where the two victims were found.
Police added that a man with apparent self-inflicted wounds was located and detained. They believe he's connected to the two victims, but their relationship was not immediately clear.
The woman's injuries are considered critical while the two other individuals were stabilized at the hospital, police said.
A motive is under investigation.
ABC13's Neighborhood Safety Tracker shows 852 assaults were counted over the last 12 months in the designated Westchase-Woodchase Village-Point West area where police responded Wednesday night.