The country’s military said 38 people were rescued from the sinking boat on Saturday and that the child’s body had been retrieved.
“A navy patrol unit immediately headed there, retrieved the body of a five-year-old child and rescued the rest” of the passengers, a statement said.
Four of those rescued were taken to nearby hospitals with the help of the Lebanese Red Cross, the statement added.
Lebanon’s Al-Jadeed TV reported that the child who died was a five-year-old from Palestine.
Humanitarian representatives and government officials say the number is likely much higher, since many refugees who have fled Syria’s civil war to Lebanon are not officially registered with the United Nations.
Lebanese authorities have begun organising return trips to refugees willing to go back.
But UN officials say with no peace deal in Syria, it is too early for the mass return of refugees.
Syrian refugees in Turkey and Lebanon have been using small boats to take them to Greece or Cyprus in the hope of claiming asylum in the EU.