Jukich was originally drafted by the Oakland Athletics in the 13th round of the 2006 MLB Draft. During the 2006 season, Jukich went 3–2 with a 2.52 ERA in 16 games pitching primarily for the Vancouver Canadians. In 2007, Jukich was sent to the Cincinnati Reds to complete an earlier trade. He pitched in the Reds' organization until 2010 eventually reaching AAA. In 2010, he compiled a 7–4 record with an earned run average of 3.90. On December 12, 2009, Jukich was selected by the St. Louis Cardinals in the Rule 5 Draft, though he was eventually returned to the Louisville Bats. In the fall of 2010, while Jukich was pitching for Los Leones del Caracas in Venezuela, he was informed that the Reds had sold his contract to LG Twins of the Korea Professional Baseball league.
Jukich played three seasons with the Twins. Overall, he posted record of 25-22 with an ERA of 4.00.