Jeřábek played as a youth with hometown club, HC Plzeň. Undrafted, he remained in the Czech Republic and made his senior debut with Plzeň in the Czech Extraliga during the 2008–09 season. Over the following three seasons, Jeřábek continued his development before cementing a full-time role on the blueline of Plzeň in the 2012–13 season. In establishing himself as the club's top defenseman, Jeřábek was recognised in the 2015–16 season, as the league's best defenseman in compiling 33 points in 52 games with Plzeň. In order to play at a higher level, Jeřábek left Plzeň after 8 senior seasons in signing a one-year contract with Russian outfit, Vityaz of the Kontinental Hockey League on 5 May 2016. In the ensuing 2016–17 season, Jeřábek instantly assumed the role as Vityaz's top pairing defenseman. He led the blueline with 5 goals and 29 assists for 34 points in 59 games, placing him 6th in overall scoring. He was also selected to represent Vityaz at the 2017 KHL All-Star Game. In attracting NHL interest and at the conclusion of his contract with Vityaz, Jeřábek signed a one-year, entry-level contract with the Montreal Canadiens on 1 May 2017. In the 2017–18 season, Jeřábek was initially assigned to AHL affiliate, Laval Rocket. On 22 November 2017, he received his first recall to the NHL. He appeared in 25 games with the Canadiens before on 21 February 2018, Jeřábek was traded to the Washington Capitals in exchange for a fifth-round pick in the 2019 NHL Entry Draft. Jeřábek played in 11 games during his first season with the Capitals, and scored his only goal with the Caps against his former team in a March game against the Canadiens. Jeřábek also started the first two playoff games of the first round against the Columbus Blue Jackets during the Capitals' 2018 Stanley Cup run, but was subsequently scratched for fellow rookie Christian Djoos. As a free agent from the Cup winning Capitals, Jeřábek was signed to a one-year contract with the Edmonton Oilers on 20 August 2018. Before starting the 2018–19 season, Jeřábek was traded to the St. Louis Blues for a conditional 6th round draft pick in the 2020 NHL Entry Draft. He played in a single game with the Blues, before he was placed on waivers and re-assigned to AHL affiliate, the San Antonio Rampage, for the remainder of the season. On 3 May 2019, as an impending free agent from the Blues, Jeřábek opted to leave the NHL and return on a one-year contract to Russian club, HC Vityaz of the KHL.
