Twenty-two people were taken to nearby hospitals by emergency responders, Pena said, adding that of those patients, 11 were in cardiac arrest.
More than 300 people were treated at a "field hospital" at the NRG Park, where the festival was being held, he said.
About 50,000 people were at the festival, Pena said.
"The worst of the incident began around 9.15pm [local time] when the crowd of approximately 50,000 began to move towards the front of the stage," ABC Eyewitness News 13 quotes Pena as saying.
"The crowd began to compress toward the front of the stage, and people began to panic," Pena told the news organisation.
Organisers paused the concert when it was apparent multiple people were hurt, they reported.
"The deadly incident came hours after a massive crowd stormed the perimeter of NRG Park prior to the evening incident, creating a chaotic situation for security personnel and event staff," ABC Eyewitness News 13 reported.
The two events were reportedly not related.
"Our hearts are broken," Judge Lina Hidalgo of Harris County said at the news conference. "People go to these events looking for a good time," she said, adding, "It's not the kind of event you where you expect to find out about fatalities."
Travis Scott, a rapper, launched the Astroworld Festival in 2018, and it has been held annually since. The lineup included such acts as Lil Baby, Metro Boomin and Roddy Ricch.