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The shooting appears to be "a domestic situation that is isolated," a tweet from Austin police said.
Police identified the suspect, still at large, as Stephen Nicholas Broderick, 41.
It is unknown if Broderick fled on foot or in a vehicle, and authorities are concerned that he could be hiding or take a hostage, according to Austin Police Interim Chief Joseph Chacon.
"Obviously this is tragedy. We have people who have lost their lives out here," Chacon said. "The danger still remains high at this point."
Broderick is a former Travis County Sheriff's Office detective who was charged with the sexual assault of a child, Travis County Sheriff's Office spokeswoman Kristen Dark told CNN.
Dark said Broderick resigned from the department last year after he was arrested and charged with sexual assault of a child. He was arrested June 20 and released on bond the same month.
CNN has reached out to the Travis County prosecutor for more information and is working to obtain the affidavit in the case.
The shooting was targeted and the three victims -- two women and one man -- knew Broderick, according to Chacon. A child was involved but has been located and is safe, he added.
Residents are advised to continue to shelter in place as the search for the suspect continues, Chacon said.
The suspect's motive is currently unknown.
This is a developing story and will be updated.