Columbia police Chief WH "Skip" Holbrook said the suspect, a 33-year-old man with a lengthy criminal record, also died.
The dead officer, 29-year-old Christopher DeLong, had been with the police department for two years and leaves behind a wife and two young children, Holbrook said.
"Our hearts are broken this evening," he said, appearing to be choked up at times.
DeLong's wife, in a social media post, praised her husband as the "best dad to our babies" and said she was "living a nightmare".
After a Saturday night news conference, Holbrook and other law enforcement officials joined in a procession from the hospital. The second officer was in stable condition, the chief said.
"I hope that our officers know that they're not alone in this. We will lean on each other in this tragic time," Holbrook said.
"Let's pray for this department."
The shooting unfolded after a woman called police around 9:30am on Saturday saying a man who she had a restraining order against was destroying property at her home.
An officer quickly arrived on scene and learned the suspect had left. The woman gave the officer a description of the suspect and vehicle description.
Around 10:30am the officer left the home but just minutes later he initiated a call about a suspicious person after seeing a person near a vehicle that matched the woman's description, Holbrook said.
A second officer arrived as backup and minutes later radioed that officer "were hit and a suspect was down," the chief said.
The suspect was a 33-year-old man with a lengthy criminal record across multiple states, the chief said.
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