Indy Metro Police Chief Randal Taylor told the Indianapolis Star the detective will be suspended, although he didn't say for how long. When he returns he'll be assigned to a new unit. The cop's identity remains anonymous for safety concerns ... according to the Chief.

TMZ broke the story ... Reed's family told us the grief was made even worse when they heard the detective saying, "I think it's going to be a closed casket, homie" moments after Reed was fatally shot during an encounter Reed streamed live on Facebook.

During the incident, Reed was seen behind the wheel of a car before he bailed out on foot. As he ran, someone was heard yelling, "Stop, stop." Reed respond, "F**k you" ... and then shots were fired and Reed fell to the ground.

His phone was still streaming, and that's when the detective popped off with the disgusting remark.

The shooting triggered tons of protests while others, like comedian Mike Epps, called on Indy PD to act swiftly while imploring the black community to "stop giving them an opportunity to kill us."

The police chief said the investigation into the shooting is ongoing.