Barikzai said Younus, a member of Afghanistan's upper house of parliament representing Baghlan, failed to stop at a police checkpoint set up as part of a planned ambush of Taliban fighters.
"They continued to drive after being ordered by police to stop so the police opened fire," an interior ministry statement said.
"Unfortunately the senator and his driver were killed and a third person accompanying them was wounded."
The statement said the ministry had opened an investigation.
Officers were hiding in an area near Pul-e-Khumri, where they expected fighters to transport a Taliban commander wounded in fighting on Tuesday, local police said.
That clash left four police officers and four fighters dead, according to police.
The security situation in northern Afghanistan has deteriorated over the past year, with government authority consistently challenged by Taliban-linked fighters.
Around 113,000 international soldiers are battling the intensifying uprising under US and Nato command, with a new strategy aiming to hand over more authority to Afghan security forces.
In the past four years, direct fire or suicide attacks have killed one senator and 10 other MPs.
Wednesday's incident is the first in which Afghan police have killed a senator accidentally.