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.

The Bruins started Cehlarik at their American Hockey League affiliate in Providence, but he earned a midseason callup and made his NHL debut against the Vancouver Canucks on Feb. 11, 2017. Cehlarik wound up spending 11 games with the Bruins, finishing with two assists. He had 38 points (20 goals, 18 assists) in 49 AHL games.

Cehlarik began 2017-18 with Providence, but was called up in mid-November and scored his first NHL goal against the San Jose Sharks on Nov. 18, 2017. He spent much of the remainder of the season in Providence, a victim of a numbers game on a team with a host of young forwards.