Cpl. Tracey Knight of the Fort Worth police said Ed Russell McIver Sr., who was wanted on several felony warrants, was killed.
His son was caught later in a field, Police Chief Chief Joel Fitzgerald said. Ed Russell McIver Jr. was captured without incident, police tweeted.
The Fort Worth Police Department identified the injured officer as Matthew Pearce, a seven-year veteran. He was shot multiple times and is in critical condition, according to a press release from the department.
"He's being watched every minute, being watched very closely. Time is our friend," Robert Earley, the chief executive officer of JPS Health Network, said.
Fitzgerald told reporters at an earlier news conference that the officer was "very lucky."
The officer was not identified, because family members were still being notified.
Knight said a uniformed officer, at the request of the undercover fugitive task force, tried to make a traffic stop. A 15-minute car chase ensued and it ended with the two suspects running from a vehicle into a heavily wooded area.
The patrol officer and others followed.
Residents in the area were asked to stay inside. CNN affiliates KDAF
reported the shooting took place in west Fort Worth.
The suspect who was on the loose is said to be armed and dangerous. More than 100 officers were looking for him, Fitzgerald said. The search is hampered by mud and thorny underbrush, officials said.
The father was wanted on charges of aggravated assault of a family member and for aggravated assault with a deadly weapon, Kinght said. He also had two bail jumping warrants. A gun was found near him at the scene of the gunfight, Knight added.
McIver Jr. will be charged with attempted capital murder, evading arrest and unlawful carrying of a weapon.