The school trip ended in tragedy on Sunday after the children were swept out to sea by strong waves at Can Gio beach, a coastal area on the outskirts of Vietnam's second largest city.
"The last bodies were found early Monday morning,'' a policeman in Can Gio district told AFP, without giving further details.
According to the state-run Tuoi Tre newspaper, the children, aged between 12 and 14 years, were part of a group of nearly 100 students who were attending the school-organised picnic.
"Most of them could swim well,'' a teacher who was escorting the picnic group said, according to Tuoi Tre.
"Suddenly, the waves became big, pulling the kids away from the shore. Four of them swam back to ask for help but rescue canoes were not immediately available,'' he said.
The students came from Nguyen Binh Khiem Upper Secondary School in neighbouring Binh Duong province.
Drowning is one of the main causes of child death in Vietnam, with many children drowning during the hot summer months, especially in rural areas.
About 3,500 children die by drowning each year, according to Tuoi Tre figures.
Efforts to introduce nationwide swimming lessons in schools have been hampered by a lack of facilities and funding.