Staffordshire Police said officers are looking into the incident after images of the ducklings lying in the road were shared on social media
The incident happened in Trentham, Stoke-on-Trent on Friday.
The force said it was trying to establish if any offences had been committed.
Steven Walley wrote in a Facebook post: “I’ve just been driving on the A34 at Trentham Gardens roundabout when a family of seven ducklings were crossing the road.
“All the traffic stopped to let them cross but disgustingly this van driver, after initially stopping, could not then wait for the five seconds it would have taken to let them cross and drove straight over them, crushing three of them.”
Mr Walley said he had then followed the van to a nearby lay-by, and had what he described as a “very heated conversation” with the driver.
Staffordshire Police said it was aware of the post had made contact with the author.
“We have made contact with the author of the post and are establishing potential offences under the Wildlife and Countryside Act,” the force said.
“We understand this is an emotive issue for many people and we ask please that you do not take matters into your own hands.”