Earlier in the day, a teenage boy was killed and a woman was sent to the hospital with minor injuries.
Interim Chief of Police Brian Manley told KXAN the packages were average size boxes.
She said residents were on high alert - made nervous even by packages addressed to them. All rights reserved. This material may not be published, broadcast, rewritten, or redistributed.
A package blast rocked another Austin home on March 2, killing a man.
Police have said they are not sure if the devices that detonated had all reached their intended targets. In a statement issued on Tuesday, Gov. Abbot said he had been briefed on the recent blasts which have claimed the lives two people and injured two others. "The cops were running and telling everyone 'Get out of the house!"
The chief said authorities did not have a description of suspects or suspected vehicles.
People receiving unexpected packages in Austin are being urged to not handle them and to call 911. They also said her mother, Maria Moreno, was hurt. The woman injured Monday afternoon also suffered life-threatening injuries, the chief said.
Dixon said while he knew of no one who bore a grudge against his stepson, he could not help but think about his and Mason's family ties and their prominence in Austin's African-American community.
"It looked like small terrorism", he said.
In a tweet, organisers of the popular festival said they were "heartbroken" by the explosions and urged visitors to stay safe. "The substantial security operation already in place for SXSW has been instructed to be extra vigilant".
Neighbors on both sides of the home were evacuated as a precaution until they were confident that there was not a second package.
Anthony Stephan House was the March 2 victim.
The Washington Post is reporting House's stepfather, Freddie Dixon, was good friends with the grandfather of the teenager killed Monday. Both incidents are being investigated as homicides.
"We do see similarities and believe these cases are linked at this time", Manley said.
"If you've received a package that has been left on your doorstep or left in your yard or left on your driveway that you were not expecting or that was not from someone you know, then give us a call", Manley said.
Manley stated, "We are not going to tolerate this in Austin, and you have seen every stop will be pulled out...the federal agencies are with us to lend us a hand and to bring this to as quick a resolution as possible". Later in the morning, investigators at that scene had to rush miles away to respond to the second explosion, which seriously injured a woman identified by her relatives as Herrera. A cardboard box left in front of a house in the state capital, Austin, exploded when a resident took it inside and opened it.
In all three cases, police said the packages did not appear to have gone through the US Postal Service or private carriers like UPS, but were left on doorsteps without a knock or ringing of doorbells. They are collecting evidence that will be delivered to a lab for analysis.