March 27, 2017 0428 GMT
Details aren't immediately clear because no one has yet been charged with a crime. Police said Tuesday that the arrests weren't related to terrorism, AP reported.
West Yorkshire police said that the Independent Police Complaints Commission was investigating the circumstances of the man's death.
Police shootings are rare in Britain and there is an automatic investigation when someone is killed.
The man was shot Monday evening on a highway near Huddersfield, 190 miles (305 kilometers) north of London.
Police said it was a "preplanned policing operation," which suggests it was based on intelligence information.
The junction where the incident happened remains closed to traffic.