Investigators suspect five more babies - all from surrogate mothers - had been cared for at the plush suburban property but had already been taken out of Thailand by the time the nursery was discovered on Tuesday.
A Thai lawyer present during the raid told police the babies were fathered by an unnamed wealthy Japanese man.
The infants are believed to be aged between two weeks and two years, although no official documents were found with them.
Each baby had a nanny caring for them, who said they were paid $310 a month to look after the infants.
"There were 14 babies in total but five have been taken out of the country already," said investigating officer Colonel Pakphum Poolsiripoka.
"We are investigating whether human trafficking has taken place and if there has been a violation of Medical Council rules," he added. "Now we are gathering evidence and interviewing witnesses."
Another officer on the investigation team, who declined to be named, told AFP the babies were all "born through surrogacies" and the Japanese man was presumed to be the biological father.
Immigration police at Bangkok's main airport said the man at the centre of the mystery flew to Macau on Thursday on a genuine Japanese passport.
"Between 2010-14 he entered (and left) Thailand 41 times. On ten occasions he flew out to Hong Kong and Macau," Police Major-General Suwichpol Imjairach told AFP.
The man's apparent lawyer did not answer calls from AFP.
The case is the latest twist in a expanding surrogacy scandal that erupted after an Australian couple were accused of abandoning a baby born with Down's syndrome to a Thai surrogate mother - but taking off with his healthy twin sister.
Paid surrogacy is illegal in Thailand and the kingdom's army rulers have vowed to beef up laws with up to 10 years jail time for anyone found guilty of involvement in the trade.
In the case of the Down's baby - named Gammy - the Thai surrogate mother said she agreed to carry another Thai donor's egg fertilised by the Australian man in exchange for around $14,900.