Millen made over 600 appearances for six teams during his 14 NHL seasons.
The Toronto native was chosen 102nd overall by the Pittsburgh Penguins in the 1977 NHL Amateur Draft, while he was in the midst of a fine OHA career with the Sault Ste. Marie Greyhounds. He also played for the Peterborough Petes in the OHL from 1974 to 1977. In 1978–79, he looked solid in 28 games as a rookie and became a fan favourite at the "Igloo." Two years later, he won 25 games and nearly led his team to a first round upset over the St. Louis Blues, losing the decisive fifth game in double overtime.
In June 1981, the Hartford Whalers signed him as a free agent. After playing in 55 games for the Whalers in 1981–82, Millen represented Canada at the World Championships. In 1983–84, he led the NHL with 60 appearances, while toiling on one of the league's worst teams.
Millen joined the St. Louis Blues in February 1985, following a major trade that also involved Mike Liut. He formed a solid goalkeeping tandem with Rick Wamsley and helped the club reach the Conference Finals in 1986, where they were defeated in seven games by the Calgary Flames. In 1988–89, Millen registered an NHL-high six shutouts along with 22 wins. Late in his career, he spent time with the Quebec Nordiques, Chicago Blackhawks, and Detroit Red Wings before retiring in 1992.
After ending his career, Millen became the colour commentator on television broadcasts for the expansion Ottawa Senators. During his eleven seasons affiliated with the Senators, his play-by-play partners included Don Chevrier, Rob Faulds, and Dean Brown. He also paired with Chevrier as the lead broadcasting team for CTV's ice hockey coverage at the 1994 Winter Olympics.
Beginning in the 1995 season, he joined the CBC's Hockey Night in Canada. After a year with CTV Sportsnet, he rejoined HNIC in 1999–2000 as the colour commentator of the network's secondary broadcast team, first paired with Chris Cuthbert and then Jim Hughson, mostly covering the second game of weekly doubleheader and three playoff rounds. He was promoted to the lead team in 2007, working alongside Bob Cole. In this role he worked on CBC's coverage of the 2007 and 2008 Stanley Cup Finals.
In 2005, he moved from the Senators to the Maple Leafs local broadcast team, and in 2007 he became the Leafs' lead television colour commentator, working alongside Joe Bowen on Sportsnet Ontario and Leafs TV.
As of 2014 he works exclusively for Rogers Communications, both on telecasts that are part of the national television contract under the Hockey Night in Canada, Rogers Hometown Hockey or Scotiabank Wednesday Night Hockey banners, and on the half of the Maple Leafs regional package that appears on Sportsnet Ontario.
Millen's son Charlie is currently a goaltender for the Laurentian Voyageurs of the OUA (Canadian University).