Victims included the 47-year-old husband, his wife and two of their children, including a 10-year-old boy. A niece and a nephew of the couple were also killed. Their 2-year-old daughter was not harmed.
Police made one arrest and were searching for other suspects, Thanh Nien newspaper reported.
The murders were discovered at around 8:00 by a neighbour in Chon Thanh District of Binh Phuoc province, Tuoi Tre newspaper reported, around 90km north of Ho Chi Minh city.
Police told reporters that the family, which owns a woodworking factory with more than 100 workers, was apparently targeted for robbery.
Perpetrators broke into the house early on Tuesday and tied the six victims to three pillars, according to news reports.