A police spokesperson said on Sunday the suspected gunman, an Israeli Arab from the nearby Israeli city of Tayibe, was also killed and a firearm was found in his possession.
Israeli media reported a second suspect was also killed.
"Large police forces remain at the scene, and searches are continuing," the police said in an earlier statement, urging the public to remain vigilant.
Local media identified the 35-year-old dead man as an Israeli citizen.
Israel's ambulance service said the man died from gunshot wounds.
It described the incident as a drive-by shooting, with five others injured in shootings at three nearby locations, two of them seriously.
Police said they had located the suspected vehicle used.
The shootings took place near the Palestinian West Bank city of Qalqilya.
Palestinian militant group Hamas praised the attack but did not claim responsibility.
Israeli soldiers were deployed to one of the sites in central Israel and to a nearby Israeli settlement in the West Bank after the shootings, the military said.
Prime Minister Benjamin Netanyahu has been briefed, his office said in a statement.
Hardline Finance Minister Bezalel Smotrich called for a "profound change" among Israel's Arab community, saying they were a "dangerous and extremist breeding ground for terrorism".
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