The injured were the toddler's parents and a brother, said Ghassan Douglass, a Palestinian official in charge of settlement activity north of the West Bank, where the attack occurred.
The boy who died, Ali Saad Dawabsha, was about 18 months old, Douglass said.
Authorities found the words "price tag" on the walls of the house in Duma, said Luba Samri, a spokeswoman for Israeli police.
A "price tag" attack is a term used by radical Israeli settlers to denote reprisal against Palestinians in response to moves by the Israeli government to evacuate illegal West Bank outposts, according to officials.
Both Israelis and Palestinians described it as a terrorist attack, but the latter said it blamed Israel.
"We hold the Israeli government fully responsible for the brutal assassination of the toddler Ali Saad Dawabsha," PLO official Saeb Erekat said in a statement. "This is a direct consequence of decades of impunity given by the Israeli government to settler terrorism."
Israeli Prime Minister Benjamin Netanyahu said he was "shocked over this reprehensible and horrific" attack.
"Israel takes a strong line against terrorism regardless of who the perpetrators are. I have ordered the security forces to use all means at their disposal to apprehend the murderers and bring them to justice," he said.
Ahmad Asaf , a spokesman for Palestinian political party Fatah, also blamed the attack on the Israeli government. He urged the United Nations to take steps toward justice.
A preliminary investigation shows suspects entered the village at night, set homes ablaze and sprayed graffiti on them.
"This attack against civilians is nothing short of a barbaric act of terrorism. A comprehensive investigation is underway in order to find the terrorists and bring them to justice," said Lt. Col. Peter Lerner of the Israeli Defense Forces.