The resignation of Rifi, a longtime critic of the Shiite Hezbollah, comes two days after Saudi Arabia halted deals worth USD 4 billion aimed at equipping and supporting Lebanese security forces.
The move came after Lebanon failed to back the Sunni kingdom in its spat with Shiite powerhouse Iran, the leading backer of Hezbollah.
The six-nation Gulf Cooperation Council backed the Saudi decision, raising concerns it could have repercussions for thousands of Lebanese living in Gulf countries.
The Saudi decision came after Lebanese Foreign Minister Gibran Bassil declined to support Saudi resolutions against Iran during two meetings of Arab and Muslim foreign ministers.
Also Read
Bassil is the president of the Christian Free Patriotic Movement, a key ally of Hezbollah.
"He (Bassil) dared to offend the kingdom of Saudi Arabia at the request of Hezbollah," Rifi said in a statement announcing his resignation.
"The practices of Hezbollah's statelet and its allies are not acceptable and staying in the government means approving them."
"There is an armed party that is dominating the government's decisions," Rifi said.
"I call upon the government to at least apologize to the (Saudi) kingdom, its leadership and people."
Lebanon has had a national unity government since 2014, with members of different factions including Hezbollah and the Saudi-backed Future Movement headed by former Prime Minister Saad Hariri.
Hariri returned to Lebanon earlier this month. He had spent much of the past five years outside the country after his government was brought down by Hezbollah and its allies in early 2011.
The Saudi-backed March 14 coalition is scheduled to hold a meeting later today.
It was not clear if more steps will be taken.