The massacre took place on Saturday at a Walmart store near the Cielo Vista Mall in the city of El Paso, a few miles from the US-Mexican border, the BBC reported. El Paso's population of 680,000 people comprise 83 per cent of Hispanic descent.
El Paso Police Chief Greg Allen said reports of an active shooter were received at 10.39 a.m., and law enforcement officers were on the scene within six minutes.
The Walmart was full of shoppers buying back-to-school supplies at the time of the attack.
The identities of the victims were yet to be ascertained but Allen told the media that "ages and genders of all these people injured and killed are numerous in the age groups", adding that the tragic incident could be dubbed as "hate crime".
Mexican President Andres Manuel Lopez Obrador said on Twitter that three Mexicans were among those killed in the shooting spree. But this is yet to be confirmed.
Meanwhile, the suspect who is in custody was a resident of the Dallas-area city of Allen, about 1,046 km east of El Paso, the police chief said, adding that authorities were looking at potentially bringing capital murder charges against him.
Although Allen did not identify the suspect, a law enforcement source has named him as Patrick Crusius.
Crusius reportedly attended Collin College in McKinney, Texas from fall 2017 through spring 2019.
The District President of the school, Neil Matkin, issued a statement saying that Collin College was "saddened and horrified by the news".
"Collin College is prepared to cooperate fully with state and federal authorities in their investigation of this senseless tragedy. We join the Governor and all Texans in expressing our heartfelt concern for the victims of the shooting and their loved ones," Matkin said.
CCTV images said to be of the gunman and broadcast on US media showed a man in a dark T-shirt wearing ear protectors and brandishing an assault-style rifle.
El Paso Police and the Federal Bureau of Investigation (FBI) were investigating whether an anonymous white nationalist "manifesto", shared on an online forum, was written by the gunman, reports the BBC.
The document said the attack was targeted at the local Hispanic community.
While addressing the media later Saturday, Governor Greg Abbott described it as "one of the most deadly days in the history of Texas".
"We as a state unite in support of these victims and their family members... We must do one thing today, one thing tomorrow and each and every day after this - we must unite."
President Donald Trump described the attack as "an act of cowardice".
"I know that I stand with everyone in this country to condemn today's hateful act. There are no reasons or excuses that will ever justify killing innocent people," he wrote on Twitter.
Walmart tweeted that it was "in shock over the tragic events" and was "working closely with law enforcement".
The attack came less than a week after a teenage gunman killed three people at a California food festival.
Saturday's shooting has been dubbed the eighth deadliest in modern US history.
( With inputs from IANS )