The tweet posted on Monday read: "When we have to tell someone their family member has died in a crash," accompanied by a GIF showing actor Steve Carell - playing Michael Scott from The Office - with an awkward grimace on his face.
The GIF was captioned: "This is the worst!"
The post was later deleted, but not before social media users noticed the clumsy mistake.
"You guys joke about telling people their family members have died?" another wrote.
New Zealand Police Deputy Chief Executive of Public Affairs Jaren Jones later issued an apology.
"NZ Police issued a road safety tweet which was quickly deleted after we realised the imagery was wrong and insensitive," she told SBS News.
"We feel terrible about this mistake, as we put victims at the heart of what police do.
"Social media is a hugely important channel to NZ Police and we appreciated the prompt feedback we got from members of our community who pointed out the inappropriateness of the tweet. We are extremely sorry and will learn from this."
The tweet follows a lethal weekend on New Zealand's roads with at least nine people killed.
