The Stena Line ferry arrived in Rosslare in Co Wexford in the Irish Republic at around 3pm on Thursday from Cherbourg in France.
All those found by an employee were in good health and have been moved to a passenger lounge, the ferry company said.
Two ambulances and several doctors' cars and police cars drove onto the ship's vehicle deck shortly after it docked in south-east Ireland.
A large police and Immigration Bureau presence was visible around the port.
Ian Hampton, Stena Line's chief people and communications officer, confirmed an employee discovered the people during a routine inspection, reportedly after banging was heard on the side of the trailer shortly before 10am on Thursday.
He said: "During the Stena Horizon's 9pm sailing from Cherbourg, France, to Rosslare in the Republic of Ireland on Wednesday November 20, one of our employees during a routine inspection discovered 16 people in a sealed trailer on the vehicle deck.
"All the individuals are reported to be in good health and have been moved to a private passenger lounge on the ship where their wellbeing is the focus of our employees.
"Stena Line has alerted security and immigration officials in Rosslare so as the necessary arrangements can be made for the group on the vessel's arrival in Rosslare."
Officers are expected to carry out assessments and searches of the container.
A source inside the Irish Government told the PA news agency that officials in the Justice Department were only made aware of the incident after media reports.
Opposition party Fianna Fail's spokesman on justice Jim O'Callaghan expressed his shock and demanded a full investigation into the incident.
"A full investigation must be launched into the discovery of up to 16 people being transported in the back of a lorry to Ireland," he said.
"Human trafficking is a modern form of slavery and needs to be tackled with fully resourced policing.
"Recent events show unfortunately Ireland is playing a significant part in this crime. These traffickers have to be thoroughly policed so vulnerable people are protected."
The incident comes just days after a group of 25 people were found inside a refrigerated container on board a UK-bound ship just off the coast of the Netherlands.
Last month, 39 people were found dead inside a container in Essex which had arrived in the UK via a ferry from Zeebrugge, Belgium.