After his rookie year with the Voltigeurs, Kulikov was drafted by the Florida Panthers 14th overall in the 2009 NHL Entry Draft, and was later signed to a professional contract with the club on 29 September 2009.[2]
Despite his age, Kulikov managed to play in 68 games with Florida in his rookie season, 2009–10, displaying high levels of skill and confidence. Panthers General Manager Dale Tallon expressed that the Panthers organization had high expectations of Kulikov for the future.[3]
On 18 July 2014, Kulikov signed a three-year, $13 million contract extension with the Panthers, worth $4.3 million annually.[4]
On 25 June 2016, Kulikov was traded to the Buffalo Sabres, along with the 33rd overall pick in the 2016 NHL Draft in exchange for defenceman Mark Pysyk and picks 38 and 89 in the 2016 draft.[5] In the 2016–17 season, Kulikov's time with the Sabres was largely affected through injury. In the last year of his contract, he appeared in 47 games to produce a career low 2 goals and 5 points.
On 1 July 2017, as a free agent from his disappointing tenure with the Sabres, Kulikov was signed to a three-year, $12 million contract with the Winnipeg Jets.[6]
After the completion of his contract with the Jets, Kulikov left as a free agent and on 22 October 2020, he was signed to a one-year, $1.15 million contract with the New Jersey Devils.[7] In the pandemic delayed 2020–21 season, Kulikov brought a sound defensive game to the Devils, registering 2 assists through 38 regular season games. With the Devils out of playoff contention, Kulikov was dealt at the trade deadline to the Edmonton Oilers in exchange for a conditional fourth-round selection in 2022 on 12 April 2021.[8]
At the conclusion of his contract with the Oilers, Kulikov left as a free agent and on 28 July 2021, was signed to a two-year, $4.5 million contract with the Minnesota Wild.[9]
After one season with the Wild, Kulikov was traded to the Anaheim Ducks for future considerations on 31 August 2022.[10]
As a free agent from the Penguins, Kulikov opted to return to his original club after seven seasons away, signing a one-year, $1 million contract with the Florida Panthers for the 2023–24 season on 1 July 2023.[12] After winning the Stanley Cup with the Panthers, Kulikov signed a four-year contract to stay with the Panthers.