Ryan Allen Walter Jacob 45, was shot after police responded to reports of a man with a knife in the area. He was transported to hospital but died soon after his arrival.
Jacob was the son of Squamish First Nation Chief Gibby Jacob, his family has confirmed.
"We are deeply saddened by the tragic and sudden loss of our son Ryan Jacob. This news has sent a shockwave through our family and our community," said a statement issued by the family on Friday.
"He was not only our son, he was a loving father, brother, uncle, nephew and cousin, a sportsmen and an artist.
"We are still trying to process this information and we ask that our family is afforded the time and privacy necessary to respectfully mourn our loss."
The Independent Investigations Office is handling the case.