Čajkovský made his European Elite debut during the 2009–10 season playing in the Slovak Extraliga with HC Slovan Bratislava.

[2] On 19 June 2015, Čajkovský returned to Europe and signed a one-year contract with Czech Extraliga team, HC Sparta Praha.

[3] In the 2015–16 season, Čajkovský made an immediate impact from the blueline with Sparta, compiling 11 goals and 28 points in 49 games.

[4] After attending the Carolina Hurricanes' training camp on a try-out basis, the club signed Čajkovský to a one-year, two-way contract worth $650,000 on 27 September 2018.

[7] Čajkovský played two seasons with HC Sibir Novosibirsk before leaving to sign a two-year contract to remain in the KHL with Spartak Moscow on 3 May 2023.