"The enemy infiltrated (Chad) from the Nigerian side (of the border) to attack positions of the Chadian forces," Chad's army chief said in a statement read by his deputy spokesman, lieutenant-colonel Adjani Djibrine.
"The army deplores the 11 deaths and 13 wounded," it said.
The army also said 17 Boko Haram fighters died in the fighting following the pre-dawn strike.
"Boko Haram members attacked our positions at 4:30 am (0330 GMT) in Kaiga Ngouboua about two kilometres (about a mile) from the Nigerian border" in the area of Lake Chad, a security source who requested anonymity told AFP.
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Since the start of the year, the Chadian army has been on the front line of a regional military operation against Boko Haram whose attacks have spread from northeast Nigeria, its traditional stronghold, to the neighbouring countries of Chad, Niger and Cameroon.
Boko Haram, which is affiliated with the Islamic State group operating in Syria and Iraq, has been hit hard by the offensive, losing territory, but has launched attacks and bombings in response.
Cameroon is regularly targeted by suicide bombers.
Attacks also continue unabated in Nigeria, where at least 18 people were killed and 41 injured in twin bombings on Friday on the outskirts of the capital Abuja.