Kryvyi began his career in 2012 with FC Ternopil in the Ukrainian Football Amateur League.[1] He would play in the professional realm with Ternopil in the Ukrainian Second League.[1] In his debut season in the third tier, he would make 5 appearances.[2] He re-signed with Ternopil the following season and aided the team in securing promotion to the Ukrainian First League.[3][4] He would play in 6 matches throughout the 2013-14 season.[2]
In his first season in the country's second-tier league, he played in 12 matches.[2] During the 2015-16 campaign, he participated in the 2015–16 Ukrainian Cup where Ternopil faced Shaktar Donetsk.[5] The 2016-17 season marked his fifth and final season with Ternopil.[6][7] He would initially miss the opening section of the season due to an injury.[8][9][10][11] In his final season in the second tier, he played in 21 matches.[2]
After Ternopil was relegated in 2017, he returned to the amateur level to play with Nyva Terebovila.[12][13] He departed from Nyva in the autumn of 2017.[14] Shortly after he returned to the Ukrainian Second League to sign with Nyva Ternopil.[15][16] In his debut season with Nyva, he played in 7 matches.[2] After two seasons with Nyva, he declined to renew his contract with the club in order to pursue other options abroad.[17]
In 2019, he played abroad in the Canadian Soccer League with FC Ukraine United.[18][19] In his debut season with the western-Toronto side, he finished second in the team scoring charts with 6 goals.[20] Kryvyi would help Ukraine United secure a postseason berth by finishing third in the First Division.[21] Their opponents in the first round of the playoffs were Hamilton City and succeeded in advancing to the next round where they defeated SC Waterloo Region.[22][23] The club's victory over Waterloo advanced Ukraine United to the CSL Championship final where they were defeated by Scarborough SC.[24]
Following his brief stint in the southern Ontario circuit, Kryvyi returned to Ukraine in 2020, where he played in the regional Ternopil amateur league with Buchatsk Kolos and Medobory Zelene.[25][26] He returned to his former club Ukraine United where he played the 2021 season in the Ontario Soccer League.[27]