Nate Weekley is also the brother of a Detroit officer who was charged with involuntary manslaughter in the accidental shooting of a black girl during a raid years ago.
Weekley was disciplined after posting remarks on Facebook in response to the fatal shooting of five officers in Dallas last week. He wrote that he had considered taking a day off after the "outrageous act perpetrated against my brothers."
"The only racists here are the ... Black Lives Matter terrorists and their supporters," said Weekley, who also used a crude word to describe the group as excrement.
"When we voice an opinion contrary to the department's mission, the department's goals, that's a problem. ... Social media can be our friend. But if you want to inject personal opinions, we will take quick and prompt action," the chief said.
Separately, Craig said the department is investigating online comments by a black police supervisor. He declined to elaborate.
Detroit is 80 per cent black. Across the country, the deaths of unarmed black males by police have inspired protests under the Black Lives Matter moniker. Craig noted there was a peaceful demonstration in the city Friday night.