Eleven people managed to swim to shore and were rescued but the rest are believed to be trapped underneath the boat.
Search and rescue is ongoing in the remote location near a timber concession camp called Kem Kelubuk even though nightfall has turned the place pitch dark.
The body of the five-month-old baby has been sent to the Bintulu Hospital for post-mortem.
Survivors have also been sent to the hospital.
The incident, which is said to have happened at about 2pm, is the worst river tragedy in Sarawak.
The Sarawak police, the Fire and Rescue Department, the Fisheries Department, the Marine Police and a local community organisations and longhouse folks are now involved in a frantic search and rescue operations.
The nearest settlement is Rumah Ado, a Punan longhouse located at least two hours by timber track from Tatau Bazaar which is some 120kms from Bintulu town, 220kms from Miri.
Police in Bintulu, which is the nearest urban centre, have rushed dozens of men, vehicles and equipment to help their counterpart in the Tatau district police station, said Bintulu Police Chief, Supt Sulaiman Abdul Razak.
"All government departments, voluntary groups and community associations from here and Tatau are helping out in the search and rescue efforts,'' he said.
The place gets very dark by 6.30pm.
Former Catholic priest of Belaga, Michael Jok, who is now a social activist, said he heard from his contacts in Tatau that those missing could be trapped beneath the capsized boat that had rammed into the timber-barge.
It is learnt that aside from native villagers, the express boat was also carrying government officers who were carrying out site survey in the remote interior.
As at 7.30pm on Monday, confirmed reports coming out from Tatau said that the 11 rescued - eight adults and three children - were being rushed to the Bintulu Hospital.
