Police dispatchers said they received a call requesting medical assistance for a man experiencing chest pains on Cypress Drive.
They dispatched rescue and police due to the incident possibly involving a disturbance.
When first responders arrived on the scene and first made contact with the man, they said he became combative and chased them with a sword.
Police said when they arrived, they saw the man waving the sword in the entrance of a home.
Officers then ordered the suspect to drop the weapon. Police said when the man refused, they unsuccessfully used a Taser.
That's when police said the man advanced towards them with the sword. An officer fired three rounds, striking the man in the leg.
The man was then taken to the hospital with non-life threatening injuries.
The Humble Police Department and the Harris County District Attorney's Office are investigating the incident.