The 35-year-old passed away in Cushendall, Northern Ireland, over the weekend, surrounded by his friends and family.
Almost 10 years ago, Neeson also lost his wife, British actress Natasha Richardson, to a head trauma accident when she was skiing and fell in Quebec.
Ronan Sexton, a son of Neeson's sister Bernadette, was 35 years old.
Sexton's death comes five years after he sustained a 20-foot fall that resulted in a severe head injury.
Newspapers reported that he had climbed on top of a telephone booth and fell about six metres to the ground.
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Sexton was taken to a nearby hospital where he was in critical condition at the time and later transferred to a specialist neurological center.
His family has asked for privacy as they mourn their loss, according to a statement from parish priest Father Luke McWilliams.
Neeson has not remarried since losing his wife in 2009.
The stage and screen actor died two days after hitting her head in a fall during a ski accident.
"I went in to her and I just told her I loved her".
She died from an epidural hematoma on March 18 at the age of 45.