The overnight killings, which cost the life of a civilian along with two customs officials, two forestry agents and the soldier, occurred when " elements attacked an advanced post of the Chad army" in Gabalami in the country's far west, the source said.
The attackers were "repelled" but managed to escape without suffering losses, the source added.
Boko Haram, a militant movement opposed to Western influence and seeking an Islamic state based on Sharia law, has caused the deaths of at least 20,000 people since it took up arms in 2009 in Nigeria.
Neighbouring Chad has seen a recent increase in attacks by the group.
Last month, Chad's national television reported that three of the country's soldiers had been killed during a clash with the jihadists, without giving the location.
It came as fighting took place between Boko Haram and Multinational Joint Task Force (MNJTF) soldiers in Arge in Nigeria's Abadam district, which is on the Chad border.
A Chadian soldier, as well as 20 Boko Haram members, were killed in another clash in late March in the restive Lake Chad region.
Two more soldiers were killed in an ambush in the same area a month earlier, in the first Boko Haram attack on Chadian soil since May 2017, in which nine soldiers died.
Chad, Cameroon and Nigeria have all joined the military effort by Nigeria to crush Boko Haram.
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