Oliver Scullion died at the Hilden Brewery in Lisburn, County Antrim, on Thursday. It is understood the boy was crushed under a metal tank.
His grandfather said: "Oliver was a beautiful child, full of life and enthusiasm for everything he did."
The family announced the cancellation of a planned beer festival at the site.
In a statement released on behalf of the Scullion-Hanna family, Oliver's grandfather Seamus Scullion thanked "all who are supporting us at this heart-breaking time".
"It is difficult to come to terms with life without him. We will miss him more than words can express," he added.
"Under the circumstances, we regretfully have to cancel the Hilden Beer and Music Festival, due to take place on 28, 29, 30 August."
Oliver was the son of brewery manager Owen Scullion, who was also hurt in the accident.
The family have appealed for privacy.
The Health and Safety Executive said on Thursday that it had been notified of the child's death and was investigating the circumstances.

It follows an unannounced inspection at the hospital in Dundonald in February.
In every area inspected, there were concerns about nurse staffing levels, patient care records and training for staff, said the RQIA team.
The report is part of the RQIA's programme of unannounced inspections across all hospital sites.
Its inspection team were advised that there was an insufficient number of junior medical staff at the Ulster Hospital, particularly at nights and weekends.
The report, however, said staff were compassionate and showed empathy to patients at all times.
The RQIA's Olive MacLeod said staff in the emergency department raised concerns about:
"RQIA's inspectors also highlighted essential equipment was not always available at busy times  and designated rooms for vulnerable patients could not always be guaranteed," she said.
"We were also concerned that routine safety rounds for patients were not carried out."
Mrs MacLeod said the RQIA recognised that increases in the number of admissions placed additional pressure on staff in ensuring the provision of safe, effective and compassionate care.
"However, it is vitally important that this continues to be delivered - even at times of such pressures," she added.
In response to the report, the South Eastern Health Trust said: "Many of the concerns raised by the inspection team were issues that we were already aware of and were working to address.
"This work continues and since the inspection, has included an increase in senior nurse leadership in our emergency department and an overall improvement in permanent nurse staffing.
"There are, however,  a number of factors which are relevant to this report, both regionally and within the trust.
"This inspection was carried out on one of the busiest weeks of the year, when all hospitals were under extreme pressure.  There is a well recognised capacity issue within the Ulster Hospital."

Unite union members had warned of strikes over bonus pay, but it has now been agreed that interim bonuses will be paid out until the end of August.
A long-term settlement will also be considered by union officials and EDF Energy, which is behind the scheme.
Hinkley Point C is expected to be operational in 2025.
Unite officer, Jerry Swain, said the interim agreement was "crucial" in providing a "breathing space" and "creating the opportunity for a long-term solution".
"I am pleased that following consultation with our stewards and members that we have been able to agree a clear path forward," he said.
"And that the prospect of industrial action, which is always a last resort, can be taken off the agenda in order to allow the panel to deliberate."
Nigel Cann, of EDF, said it has created a "very competitive reward structure" for its workforce.
"We are pleased that these interim arrangements allow constructive dialogue to continue to finalise this important agreement," he said.
"Unite has been a constructive partner in the discussions to date and I look forward to this continuing throughout the construction of the Hinkley Point C power station."
The grandfather of a four-year-old boy who was killed in an accident at their family-run brewery has said he will be "missed more than words can express".
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Concerns about staffing levels at the Ulster Hospital have been raised by the health regulator, the Regulation and Quality Improvement Authority (RQIA).
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The threat of industrial action by workers building the Hinkley Point nuclear power station has been averted due to an interim pay deal.