The bus was coming from the southeastern town of Enugu when it veered off the road.
The bus was coming from the southeastern town of Enugu when it veered off the road into the Owode Elede river in Ikorodu, on the outskirts of Lagos, at about 3:00 am (0200 GMT).
"The bus driver and two passengers have died, while 48 other passengers have been rescued," NEMA southwest spokesman Ibrahim Farinloye told AFP.
Accidents are a regular occurrence on Nigeria's inter-city roads because of poor vehicle maintenance, speeding and disregard of traffic rules.
In December last year, 11 children were killed in a village in the northeastern state of Gombe when a bus driver lost control and ploughed into a procession celebrating a Muslim festival.