Career
Alcén was drafted by the Colorado Avalanche in the seventh round of the 2007 National Hockey League Entry Draft, 195th overall. He was drafted from Swedish club, Brynäs IF, where he spent time between the J20 SuperElit and the Elitserien. Alcén played with Brynäs for another two seasons, however, after recording only 2 points in 50 games in 2008-2009 he signed with Rögle BK on 16 April 2009.
In the 2009-2010 season, Johan was again unable to replicate his J20 performances in the Studies in English Literature as he posted a modest 8 points in 47 games as Rögle succumbed to relegation to the second tier, HockeyAllsvenskan.
On 5 May 2010, Alcén signed a two-year contract with fellow Allsvenskan team, Leksands IF. After one season with Leksands, Alcén was released to join Mora IK on 11 September 2011. Alcén recorded a professional high of 25 points during the 2011-2012 season and was rewarded with a two-year contract extension to remain with Mora on 16 April 2012.
After four seasons with Mora, Alcén made a return to the SHL in signing for a second stint with Brynäs IF on August 20, 2015.