Media playback is not supported on this device
Fraser, the world number 90, hit nine birdies to finish with an eight under par 63, three shots ahead of the field.
More than half of the men's world's top 10 pulled out of competing at Rio 2016, citing the Zika virus.
Briton Justin Rose, one of a group on four under, hit the first ever Olympic hole-in-one on the par-three fourth.
"There is always an element of luck but you could chalk it up as a good hole-in-one," said Rose.
"I won a car that time [his last hole-in-one] but this is definitely better, better bragging rights. When you are the first to do something no one can take that away from you. That was definitely a cool moment."
Newly crowned Open champion Henrik Stenson is tied for second with Canada's Graham Delaet on five under.
Rose is one of five men tied for fourth on four under; along with Belgium's Thomas Pieters, Gregory Bourdy of France, Alex Cejka of Germany and Spain's Rafael Cabrera Bello.
Danny Willett, who became the first British winner of the Masters for 20 years in April, finished level par with a 71.
The second round begins on Friday at 11:30 BST, but there is no halfway cut as only 60 players are in the Olympic field.
In July, Northern Ireland's Rory McIlroy said he was unlikely to watch television coverage of the Olympic golf competition, preferring "track and field, swimming, diving, the stuff that matters".
Subscribe to the BBC Sport newsletter to get our pick of news, features and video sent to your inbox.
Australia's Marcus Fraser claimed a commanding first round lead in Rio, as golf returned to the Olympic Games for the first time since 1904.