A Pakistani officials told the media that the incident occurred in Bajaur Agency's Loye Mamond area.
A senior official died in the blast along with five others.
On August 22, Trump indicated that single-minded approach would extend to USA relations with troubled ally Pakistan, which consecutive United States administrations have criticized for links with the Taliban and for harboring leading militants.
The levy personnel was on routine patrolling of the area when the militants detonated an improvised explosive device through remote control as their vehicle reached the spot, it said.
A few hours after the blast, the Tehreek-e-Taliban Pakistan (TTP) terror group, also known as Pakistani Taliban, released a statement, claiming responsibility for the attack.
Bajaur Agency has seen intense fighting between militants and security forces in the past. Security in the region has improved in recent years after the Pakistani military mounted offensives there against the al Qaeda-linked Pakistani Taliban, which is considered the country's biggest security threat.
Prime Minister Shahid Khaqan Abbasi said this week it is "unfair" to blame his country for troubles in Afghanistan, adding that the USA should have greater respect for its efforts to combat militancy.