Oliver Scullion, son of the manager of Hilden Brewery, died in the incident at the premises on Grand Street.
It is understood he was crushed under a large metal tank. The boy's father is also believed to have been injured.
The Health and Safety Executive is investigating. In a statement, the boy's family said they were "deeply upset" and requested privacy.
SDLP councillor Pat Catney, who is a close friend of the family, said the child was "a force of nature".
"This little blond four-year-old wonder enchanted everyone who met him," he said.
"He was part of the life here at the brewery and I know that the staff are also devastated at his death."
The Health and Safety Executive said in a statement on Thursday it had been "notified of the death of a young child at a commercial premises in the Lisburn area and is investigating the circumstances".
It added: "We are unable to comment further at this stage except to offer our deepest sympathy to the family."
Established in 1981, Hilden Brewery is billed as the oldest independent brewery on the island of Ireland.
A four-year-old boy has been killed in an accident at a family-owned brewery near Lisburn, County Antrim.