"The current government is unable to remedy the dangerous situation in the country," Farid al-Khazin said in a statement on Friday.
"There is no substitute for national dialogue on the basis of the Taif agreement," he said, referring to a deal that ended the 1975-1991 civil war and committed Syria to moving the troops it keeps in Lebanon to the eastern Bakaa Valley.
The government has come under intense pressure from Lebanon's opposition to resign since al-Hariri was killed in a bomb blast in Beirut on Monday. Fourteen others were also killed.
Blaming the government
Opposition figures have blamed the government and its Syrian backers for al-Hariri's death, calling for the cabinet to quit and for Syria to withdraw its remaining 14,000 troops from Lebanon.
The government has rejected the demands and Syria has denied killing al-Hariri.
"The current government is unable to remedy the dangerous situation in the country"
Al-Khazin, a Maronite Christian, joined the government formed by Prime Minister Umar Karami after al-Hariri resigned in October amid bitter disagreements with Syrian-backed President Emile Lahud.
Al-Khazin said he would hold a news conference on Saturday to explain more fully the reasons for his resignation.
The assassination of al-Hariri has been seen as a serious setback to tourism in Lebanon, which had been recovering as the country was rebuilt after the civil war.