The two suspects, a man and a woman detained Saturday in the southern province of Dong Nai, had confessed to buying the babies at hospitals in the south of the country, according to the VietnamNet online news website.
They then resold them to another Vietnamese for between four and 12 million dong (about 225 to 675 dollars).
VietnamNet did not specify whether the babies were intended for international adoption or not.
Dong Nai police could not be reached Monday evening to confirm the report.
In September, six Vietnamese were jailed in northern Vietnam for their roles in a graft scandal which saw hundreds of babies adopted by foreigners.
In that case false documents of abandonment were assembled to allow the adoption of more than 200 infants by foreigners between 2005 and 2008, according to media reports.
Vietnamese centres working with France, Italy and the United States were implicated in the case.
The scandal came to light last year after the US embassy in Hanoi detailed endemic baby-selling and graft in Vietnam's adoption system.
That US report led Vietnam to suspend a bilateral adoption agreement and several other countries have raised questions over adoptions in Vietnam.