A member of the public was also shot when snipers opened fire on police during a rally in downtown Dallas, killing five officers and wounding six.
A family member says the protester who was shot was shielding her sons when she was injured.
A sister of Shetamia Taylor, 37, said Taylor was at the protest on Thursday night with her four sons, ages 12 to 17.
Theresa Williams said when the shooting began, Taylor threw herself over her sons.
She was undergoing surgery early on Friday after being shot in the right calf.
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Police say five officers were killed and seven injured in the shootings. The shootings happened at a protest over recent fatal police shootings of black men.
Williams said two of Taylor's sons became separated from their mother in the chaotic aftermath.
She said they were now stuck behind a police barricade at a hotel near a parking garage where police exchanged gunfire with a suspect.
