Cehlarik spent four junior seasons playing in his native Slovakia before taking his game to Sweden in 2011. He made his debut for Lulea in what's now the Swedish Hockey League during the 2012-13 season and helped the team win the Champions Hockey League title in 2014-15.
Cehlarik's first two seasons in Sweden, spent most with Lulea's junior team, were enough to convince the Boston Bruins to select him in the third round (No. 90) of the 2013 NHL Draft. But he stayed in Sweden through the end of the 2015-16 season, finally signing with the Bruins on June 16, 2016.