He played in the Czechoslovak First League for Inter Bratislava and Dukla Banská Bystrica.

Jurkemik played in his domestic Czechoslovak First League from 1973 to 1984, with two periods at Inter Bratislava interrupted by the 1980–81 season, which he spent at Dukla Banská Bystrica.

He was a participant in the 1976 UEFA European Championship, where Czechoslovakia won the gold medal, in the 1980 UEFA European Championship, where Czechoslovakia won the bronze medal, and at the 1982 FIFA World Cup.

[1] After his playing career Jurkemik became a manager, taking charge of various club sides as well as the Slovakia national football team.

He was relieved of his duties in December 2008 with the club 14th in the league and just two points above the relegation zone.