A second explosion later in the morning left an elderly woman in critical condition after she was injured picking up a package in front of her home, police said.
The twin bombings followed an initial blast on 2 March, when a 39-year-old man was killed - also after opening a parcel bomb.
"This again is the third in what we believe to be related incidents over the past 10 days," Austin police chief Brian Manley told a news conference.
"We are imploring the community, if you know anything about these attacks, it is imperative that you come forward."
The Texas governor's office offered a $15,000 reward for information leading to an arrest in the case.
"I want to assure all Texans, and especially those in Austin, that local, state and federal law enforcement officials are working diligently to find those responsible for these heinous crimes," Governor Greg Abbott said in a statement.
Investigators have found no evidence so far of a terrorism link and have yet to establish a definite motive or profile for the bomber, Mr Manley said.
Police were considering whether racial hatred was a factor.
"We have had two victims that were African American, and the victim of this latest incident was a 75-year-old Hispanic female," the police chief said.
"So, we are still working to identify whether or not that may play a role, but we are not going to rule that out."
Michelle Lee, a spokeswoman for the Federal Bureau of Investigation, which is aiding in the probe, told AFP: "Nothing had been ruled out in terms of motive."
Authorities say the packages, described as unremarkable looking boxes, were left overnight and not sent through the mail or any other delivery service.
Austin police probed the bomb blasts as some 500,000 attendees from nearly 100 countries were in Austin for South by Southwest - a sprawling event that features concerts, corporate presentations and film screenings.
Tesla founder Elon Musk, London Mayor Sadiq Khan, one-time presidential candidate Bernie Sanders and music producer Nile Rodgers are among the top speakers.
The festival's official Twitter account posted a statement saying the organisation was "heartbroken by the explosions in Austin earlier this month and today. Our thoughts are with the victims and those affected".
The police chief urged festival attendees to "be aware of what's going on".
Residents have been warned to avoid opening unexpected items left at their doorsteps and to report anything suspicious to police.
The request led to several calls to authorities, Mr Manley said in the afternoon conference, but none uncovered anything suspicious.
The Bureau of Alcohol Tobacco and Firearms said a national response team would join Austin police in the investigation.