A man suspected of fatally shooting a grandmother and her 1-year-old grandson inside a Florida grocery store before turning the gun on himself on Thursday has been identified as Timothy J. Wall.

Wall did not have any known relationship with the victims, the Palm Beach County Sheriff's Office said. They are continuing to investigate his motive.

All three were pronounced dead at the scene. 

Royal Palm Beach is about 15 miles inland from Palm Beach. 

The shooting happened late Thursday morning at a Publix in Royal Palm Beach in a strip mall and sent shoppers running from the store. 

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"I heard, ‘They’re shooting!’" shopper Juan Garcia told the Palm Beach Post. He said an employee told him to run. "I was scared. It’s sad because everything happened fast. Everyone was running, some employees were crying."

The sheriff’s office said the victims’ identities won’t be released because the family invoked Marsy's Law, which allows victims of crimes to block information that could be used to locate or harass them or their families from being made public.

The boy would have turned two years old at the end of the month, sheriff's spokesperson Teri Barbera told Fox News.

Publix, in a statement, said, "Our thoughts are with those who are impacted by this tragedy." The company added that it is cooperating with law enforcement but declined further comment. Publix is Florida's largest grocery chain and has more than 1,200 stores in the Southern United States.

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The sheriff's office said the supermarket would be closed until Saturday.

The Associated Press contributed to this report.