Coun. Mark Heyck introduced the motion, which states that weapons in space could "incite a new arms race" and "threaten the security of all human beings, including the citizens of Yellowknife."
Heyck said even though city council doesn't have a direct say in whether the Canadian government should take part in a missile defence shield, it's important to make their feelings known.
"We have a responsibility to express our opinions on this issue," said Heyck, who criticized Western Arctic MP Ethel Blondin-Andrew for not expressing any opinions of her own on the issue.
Heyck said the idea that Canada or the United States could come under attack by rogue nations with long-range missiles is ludicrous.
"It seems the Canadian military has dropped more missiles on Yellowknife than North Korea," he said, referring to an incident last summer when a Canadian fighter jet accidentally dropped a live missile on the Yellowknife Golf Club.
Coun. Kevin O'Reilly called the missile defence shield plan "immoral."
He said U.S. plans to erect missile bases in Alaska and Greenland would pose more a threat than providing any actual security.
"If anyone is a rogue state it's the United States," said O'Reilly.
"Where are they going to shoot down these missiles? They're going to come down on top of us." Other councillors were less impressed.
Coun. Blake Lyons said he couldn't support the resolution if it singled out the United States alone, noting that China and Russia have also indicated that they're building up their countries' military capabilities.
Coun. Alan Woytuik said Canada may need U.S. protection in the event of an attack because our military is incapable of doing it for us.
"I wouldn't rely on our armed forces to protect us in a world conflict," said Woytuik. "We have to depend on the Americans."
He also chided O'Reilly for his suggestion that missile bases in the High Arctic could pose a danger to Yellowknifers, suggesting that not supporting a missile defence shield would put us in the line of fire.
"If we fail to participate in this, (the U.S. is) going to put them on the 49th parallel, and then they'll fall down on us," said Woytuik.
Ultimately, council voted in favour of the motion 4-3.
The resolution will now be forwarded to the Federation of Canadian Municipalities, urging it to encourage other municipalities to adopt similar resolutions.
It will also be sent to the prime minister and ministers for Foreign Affairs and National Defence.
Reverend Liz Richards with the United Church, who petitioned council to adopt the resolution the same evening, said she was pleased it passed.
"I think it's really important that Canadian municipal jurisdictions, wherever they are, have their voices heard," said Richards.
"It's our way for the federal government to hear voices from across the country."
An aide for Blondin-Andrew said she had no comment, other than to say she held a town hall meeting on missile defence when Defence Minister Bill Graham was in town.