A Lao Airlines official said the plane had crashed near Pakse in Champasak province which is on the border of both Thailand and Cambodia.
There were reports the accident happened in bad weather as the plane was coming into land.
Thai television showed a photograph of the ATR 72 turboprop aircraft partly submerged in shallow water on a stretch of the Mekong, the tail severed.
Another television channel showed what appeared to be several bodies on the bank of the river.
Thai media said all 44 people on board, including the five crew, were killed, among them five Thai nationals.
Thai Foreign Ministry spokesman Sek Wannamethee said information on the death toll had come from the Thai Embassy in the Laos capital Vientiane.
Lao Airlines is the national carrier of the communist state and carried 658,000 passengers last year on its fleet of 14 planes, mostly propeller-driven.
It operates on seven domestic routes and has international flights to China, Cambodia, Thailand, Vietnam and Singapore.