A prayer was held next to the grave site, followed by speeches and the singing of Happy Birthday before balloons were released, Mr Jack said.
"It was a chance for everyone to reunite again after his burial and exhumation, which was devastating to go through."
Police had to exhume Israel's body in October for further tests.
Mr Jack has appealed for anyone with information about his son's death to come forward.
"We're still dealing with grief, this [Israel's birthday] does help but we still desperately need answers.
"We know that people out there have the answers and they might be afraid but what we're experiencing you wouldn't wish that on anybody so we're asking people to come forward and help."
Israel's sister Ayla Jack is raising awareness about staying safe around alcohol. She has given up drinking for Febfast to make a stand against something that had contributed to her brother's death.
As of yesterday she had raised $575 for the New Zealand Drug Foundation.