Austin-Travis County EMS said on Twitter that a patient - a woman in her 70s - was taken to a hospital "with serious potentially life threatening injuries."
Austin Police Chief Brian Manley warned residents to avoid opening unexpected packages.
"If you receive a package that you are not expecting or looks suspicious, DO NOT open it, call 911 immediately," he tweeted.
Authorities had said they believe the first two explosions are linked.
Both took place in the morning hours, and in both cases, the package was not delivered through the US Postal Service, authorities said.
In addition, both of the homes belonged to African Americans, Manley told reporters.
"So we cannot rule out that hate crime is at the core of this; but we're not saying that that's the cause as well," the police chief said.
Manley, who reportedly was on the scene of today's first explosion when he was called to the second, said local and federal law enforcement agencies would ensure "every stop would be pulled out" to solve the cases.
"We are not going to tolerate this in Austin," he said.
The Bureau of Alcohol, Tobacco, Firearms and Explosives said it was dispatching members of its National Response Team (NRT) to help respond to the explosions.
The FBI field office in San Antonio also said it was assisting Austin police with the investigation.
The latest explosions happened during the South by Southwest music, film and technology festival, which brings about 400,000 visitors to Austin each year. The explosions happened far from the festival's main events, and there was no immediate word from organisers about additional safety precautions.
- additional reporting AP
