The Houston Police Department said there was a report of a stabbing on Hillcroft Avenue about 7:45 p.m.
When officers arrived at the scene, they said they found a man lying on his apartment balcony with multiple stab wounds.
Houston Fire Department paramedics rushed the 30-year-old to the hospital, where he was pronounced dead.
Investigators said that witnesses reported seeing an unknown Black man wearing all black clothing flee the scene in an unknown vehicle.
Anyone with information in this case is urged to contact the HPD Homicide Division at 713-308-3600 or Crime Stoppers at 713-222-TIPS.