Fighters crossed Lake Chad in four motorboats and attacked a village, an army spokesman told the BBC.
The Islamist militants were pushed back by Chadian troops after killing several people, residents said.
Chad recently joined Nigeria, Niger, and Cameroon in a military coalition against Boko Haram.
The jihadists, who want to create their own Islamic caliphate in Nigeria, have killed thousands and forced millions to flee their homes in north-eastern Nigeria since 2009.
Colonel Azem Bermandoua Agouna, of the Chadian military, told the BBC’s Thomas Fessy that the militants had killed one soldier and wounded a further four in the village of Ngouboua.
Mr Agouna said a local chief was killed during the attack by a stray bullet. He did not confirm reports of other civilian casualties.
Two Boko Haram militants were killed and five injured, he said.
Residents put the number of attackers at around 30 and said they torched two-thirds of the village’s homes.
“They came on board three canoes and succeeded in killing about 10 people before being pushed back by the army,” one resident told Reuters.
Chadian military aircraft carried out air strikes against the militants in response, destroying their vessels, officials said.
Chad formed a military alliance in January with Nigeria, Niger, and Cameroon, aimed at defeating Boko Haram.
Chad, seen as having the region’s most effective military, has conducted airstrikes against the jihadist group in both Nigeria and Niger, and stationed its troops in the border areas around Lake Chad.
The Islamist militant group has intensified its attacks against Nigeria’s neighbours in response, forcing thousands of residents to flee their homes.
Boko Haram has been attacking Cameroon for nearly a year, but now it has carried out attacks in both Niger and Chad within a week, making those countries pay for their participation in a regional offensive against the Nigerian insurgency.
But can the Islamist militants fight on four fronts at the same time?
Clearly, Boko Haram wants to show that it can strike wherever it wants. But its attacks have all so far been launched from Nigeria – it has yet to gain local endorsement in neighbouring countries, which it will need in order to transform what has become a regional war into a regional insurgency.
Approximately 7,000 people fled to Ngouboua after Boko Haram attacked the Nigerian border town of Baga in January.
Boko Haram leader Abubakar Shekau denounced the president of Chad, Idriss Deby, in a video released shortly after the coalition was formed and declared “war” on Chad.
Founded in 2002, initially focused on opposing Western education – Boko Haram means “Western education is forbidden” in the Hausa language Launched military operations in 2009 to create Islamic state Thousands killed, mostly in north-eastern Nigeria – also attacked police and UN headquarters in capital, Abuja Abducted hundreds, including at least 200 schoolgirls Controls several north-eastern towns Launched attacks against neighbouring Niger and Cameroon in 2015.
The militants have also continued their insurgency in north-eastern Nigeria – at least 21 people were killed on Thursday in two separate attacks in Borno State, witnesses told AFP.
Militants killed 12 people in the village of Akida and nine in the village of Mbuta, community leader Mustapha Abbagini said.
Approximately 3.2 million people in Nigeria have fled their homes as a result of the Islamist insurgency, officials say, with many living in makeshift camps.
Nigeria launched an investigation on Tuesday after reports of rapes, child trafficking and other abuses in the camps.
The conflict with Boko Haram has forced a postponement of Nigeria’s presidential and parliamentary elections from 14 February to 28 March.