[1] After playing his first four professional seasons with Metallurg Novokuznetsk in Russia, Bobrovsky signed a three-year, entry-level contract with the Flyers on 6 May 2010.

Flyers head coach Peter Laviolette named Bobrovsky the starting goaltender for the opening game of the 2010–11 season against the Pittsburgh Penguins on 7 October 2010.

After a disappointing showing during the playoffs, however, in which he was often benched in favour of backup Brian Boucher, the Flyers signed Ilya Bryzgalov to a nine-year contract to be their new starting goaltender.

Bobrovsky was instrumental in the Blue Jackets' push for a playoff spot, which ultimately came up just short as the team finished in ninth place in the Western Conference.

Bobrovsky backstopped the Blue Jackets in the 2014 playoffs, where they played the Pittsburgh Penguins in the Eastern Conference quarter-finals.

A 37–22–6 record during the 2017–18 season was once again good enough to propel the Blue Jackets to a playoff spot as the seventh seed in the Eastern Conference.

They faced the second seeded and eventual Stanley Cup champion Washington Capitals in the first round, falling in six games.

The Blue Jackets qualified for the postseason the next year as the eighth and final seed in the Eastern Conference, behind Bobrovsky's 37 wins.

[15] He struggled through a down year, posting a record of 23–16–9 through 50 games in the 2019–20 regular season before the onset of the COVID-19 pandemic shut down the league.

In the 2022 Stanley Cup playoffs, the Panthers defeated the Washington Capitals in the first round, the team's first series win since 1996.

In the off-season, it was reported that the team was contemplating attempting to move Bobrovsky's contract, while being noted that this was difficult in light of both his salary and his no-movement clause.

[21][22] The 2022–23 season began poorly for Bobrovsky, and for the team as a whole, with many speculating that he was losing the net to backup Spencer Knight.

"[28] Lyon continued in the starting role even after Bobrovsky returned to the roster, including in the opening games of the first round playoff series against the Presidents' Trophy-winning Boston Bruins.

The Panthers then faced the Toronto Maple Leafs in the second round, winning that series in five games to advance to the Eastern Conference Final against the Carolina Hurricanes.

[30] The first game of the Conference Final went to quadruple overtime, with both Bobrovsky and Hurricanes goaltender Frederik Andersen praised for their performances, before the Panthers prevailed with seconds remaining in the seventh period of play.

Bobrovsky was named as one of Russia senior team's goaltenders for the 2014 Winter Olympics; he and Semyon Varlamov split time tending the net.

Bobrovsky faced-off against fellow NHL goaltender Pekka Rinne of the Nashville Predators in the gold medal game.

Russia went on to win that game 5–2, with Bobrovsky saving 24 out of 26 shots, backstopping the Russians to their second gold medal in the past three years in the tournament.

On 13 March 2020, Bobrovsky pledged to give $100,000 to part-time workers of the BB&T Center who were unable to work during the suspension of the 2019–20 season because of the COVID-19 pandemic.