Mikkelson, a two-time gold medallist in women's hockey, and her husband Scott Reid are expecting a son in September.
They're asking people to send baby names to @Mikkelson12 with the hashtag "#NameMyBaby."
The couple will pick their eight favourite suggestions July 6 and put them to a vote on social media.
Voting will be conducted bracket-style with quarter-finals, semifinals and a final. The bracket will be on Mikkelson's website meaghanmikkelson.com.
(A screengrab of the voting bracket now up on the site.)
They'll choose their first child's name from the two finalists.
"We've kind of been struggling a little bit to come up with names that really stand out to us and that we really, really like," Mikkelson said. "As a Canadian hockey player and a Canadian athlete we get so much support from our fans. We figured why not ask them for help?
"Each week, one baby name will face off against another. What I'll be asking my followers to do is to favourite for one name and retweet for the other. Which ever one comes out with the most votes is the one that will move onto the next round until we get down to our last two.
"People probably think we're crazy, but it's fun. It will be a fun story to tell our child."
Early suggestions Tuesday morning included Mason, Dylan and Victor.
Check out more Twitter suggestions. Story continues below:
Mikkelson won Olympic gold in 2010 and 2014. The 30-year-old defender from St. Albert, Alta., played through a broken hand suffered four days before the Olympic final in 2014.
She and Canadian teammate Natalie Spooner finished second in the second season of the reality show "The Amazing Race Canada" last year. One fan suggested Flash as a baby name because Mikkelson and Spooner were "wicked fast" on the game show.
Mikkelson and Reid have been married for four years and live in Calgary. Reid, a former goalie from Grande Prairie, Alta., played for the Western Hockey League's Kamloops Blazers and in the minor pro leagues before retiring two years ago.
It was Mikkelson's idea to tap into Twitter, but Reid warmed to the idea of deciding their son's name in a playoff hockey format.
"I'm kind of excited since we're a hockey family, it's a hockey playoff bracket," said Reid, 38. "We sit around in the spring just watching playoffs. Now we'll have playoffs into the summer."
The couple say they're prepared for bizarre and comical suggestions and perhaps a few famous hockey names.
"Maybe it's just a famous person in the world, who knows?" Reid said. "That's the kind of unique thing about this. You never know what's going to come in."
Added Mikkelson: "It takes the pressure off of us a little bit when it comes to picking a name. It is pretty hard."
Mikkelson's father Bill played for the Washington Capitals. Her brother Brendan is a former second-round pick of the Anaheim Ducks and now plays in Sweden.
Mikkelson, who plays for the Calgary Inferno in the Canadian Women's Hockey League, needed to back off training and gain weight to prepare her body for pregnancy, so she took this past season off.
She intends to return to the national women's team after giving birth. Mikkelson hopes to be ready for the Canadian team's annual January camp and the 2016 women's world championship in Kamloops, B.C., next April.
"My goal is to start training again whenever I get the green light," Mikkelson said. "I really want to make a comeback, but as many women know with pregnancy, there's a lot that's out of your control and a lot you don't decide. My body will decide that."