Maqbul bin Madi al-Sharari hit his son Mohammad "repeatedly with a cane on the back of his head and the rest of his body," the ministry said in a statement carried by SPA state news agency.
He also punched the toddler in the face repeatedly and "burned him in different parts of his body, torturing him several times, which led to his death," the ministry said.
Saudi Arabia has often faced international criticism for lacking laws that protect women and children against abuse.
Women are the main victims of domestic violence with 98 percent of physical violence committed by men against women.
Yet high number of executions in the Kingdom is also turning into a concern.
Last year, the UN High Commission for Human Rights denounced a "sharp increase in the use of capital punishment" there since 2011.
According to rights group Amnesty International, the number of executions rose from 27 in 2010, including five foreigners, to 82 in 2011, including 28 foreigners.
In 2012, the number of executions dipped slightly to 79, among them 27 foreigners.
Rape, murder, apostasy, armed robbery and drug trafficking are all punishable by death under Saudi Arabia's strict version of law.
SHI/SHI