"I don't see myself belonging to any constitutional authority in which an entire sect is absent," Sarraf, a Christian, said in his letter of resignation, according to the National News Agency.
Hezbollah has demanded greater representation in the government for itself and its Christian ally, the Free Patriotic Movement (FPM).
In particular, the Hezbollah-Amal-FPM alliance wants a third of all cabinet seats, which would give it an effective veto on cabinet decisions.
The minister handed in his resignation only hours before Fouad Siniora, the Lebanese prime minister, brought together the 24-member cabinet to discuss a UN-drafted statute for a special court to try the killers of Rafiq al-Hariri, the former prime minister.
Lahoud opposed holding a cabinet session on Monday, saying any government meeting after the resignations would be unconstitutional.
Siniora dismissed Lahoud's objections and the meeting went ahead as planned.
While the government can still assemble two-thirds of the cabinet required in order to meet and take decisions, approval of the international tribunal without the presence of the Shias could widen the political divide.
|"This is a Syrian-Iranian plan to overthrow the legitimate authority"|
On Sunday, the leader of the parliamentary majority accused Syria and Iran - which support Hezbollah - of seeking to undermine the formation of the tribunal.
Rafiq al-Hariri's son, Saad, who leads the parliamentary majority, said: "This is a Syrian-Iranian plan to overthrow the legitimate authority and prevent the formation of the international tribunal."
Four Lebanese generals, pro-Syrian security chiefs under Lahoud, have been under arrest for 14 months, accused of involvement in the murder.
A UN investigation implicated Syrian officials, but Damascus has denied playing any part in the attack in February last year in which a suicide bomber detonated explosives in a lorry.
The killing caused huge anti-Syrian protests in Beirut and led to the withdrawal of Syrian troops from Lebanon after 29 years.
Elections held afterwards created an anti-Syrian majority in the parliament and cabinet.