"I'm sick of these protesters. You are a burden on society and a blight on the community," wrote Pappert in one of at least five posts that has gone up since Sunday.
"These protesters should have been put down like a rabid dog the first night," he added.
In a reference to the Boston Marathon bombing, he also wrote: "Where is a Muslim with a backpack when you need them."
The Glendale Police Department said it suspended Pappert upon learning about the posts on Friday.
It also cancelled a neighbourhood block party for fear it might be disrupted by protesters.
"The matter is being taken very seriously and a thorough internal investigation will be conducted to determine why the posts were made," it said.
It stressed that the opinions in Pappert's posts were "absolutely" not shared by the Glendale police or city government.
On Wednesday, a police lieutenant from another St Louis suburb, St Ann, was suspended after he pointed a semi-automatic assault rifle at Ferguson protesters and, in vulgar language, threatened to kill them. Within hours, two videos of the officer's conduct went viral on YouTube, prompting the American Civil Liberties Union to demand he be removed from duty.
Meanwhile, some residents and officials trying to maintain peace worry what will happen if the grand jury now considering the case doesn't return a charge against the officer who shot Brown.
Senator Claire McCaskill's office said the Department of Justice hasn't given a timeline for the federal investigation, which centres on whether a civil rights violation occurred when officer Darren Wilson fatally shot the unarmed youth.
- AAP