The Boeing 737-800 disappeared off the radar some five minutes after taking off, shortly after its scheduled departure time of 2:10 a.m. (0010 GMT), during a thunderstorm and heavy rain, the sources said. It was heading for Addis Ababa.
Eight-two passengers and eight crew were aboard, according to the plane's manifest, the sources said.
About 50 passengers were Lebanese nationals, three with dual nationalities: British, Canadian and Russian. Most of the others were Ethiopians. Hundreds of Ethiopians work as domestic helpers in Lebanon.
According to one source, residents on the coast saw a "ball of fire" crashing off Na'ameh village, a few kilometres (miles) south of the Lebanese capital.
Senior Lebanese officials and some family members of Lebanese passengers headed to Rafik Hariri International Airport after news of the crash. The plane had flown in from Addis Ababa earlier in the night, the sources said.
State-owned Ethiopian Airlines, which could not immediately be reached for comment, has positioned itself as a major player in international air traffic in Africa and has recently expanded its Asian network.
Last Friday it announced an order for 10 of Boeing's Next-Generation 737-800s for a total price of $767 million.