Both crime scenes are now secure, Austin police say, after earlier reporting an "active shooter incident".
The shootings happened in the city's entertainment district.
Videos from the scene show a person on the ground outside a bar, surrounded by police, while officers on horseback push back a number of onlookers.
Police said in a briefing streamed online that one incident began at a bar around 02:17 local time (08:17 GMT) with a "disturbance between individuals" and that the suspect then began firing a weapon into the crowd.
A woman believed to be in her 20s was pronounced dead at the scene, while three other women in their 30s were taken to hospital with serious but not life-threatening injuries, police said.
The gunman is still at large, police said as they appealed for any video footage of the incident and its aftermath.
In the second incident only a few blocks from the first, shots were fired at a parking garage and a man in his 20s, was subsequently hospitalised after what police said was "an assault".
He is believed to be the person that fired the shots in that incident, police said.
Police said the proximity of the incidents had initially led them to think they were "dealing with an active shooter incident".
One person is dead and four others have been hospitalised after two separate shooting incidents in the Texan city of Austin, police say.