Burnes attended Centennial High School in Bakersfield, California. In 2013, his senior year, he went 9-4 with a 2.23 ERA in 22 appearances. After high school, he enrolled and played college baseball at Saint Mary's College of California. In 2015, he played collegiate summer baseball with the Orleans Firebirds of the Cape Cod Baseball League. In 2016, his junior year, he posted a 9-2 record with a 2.48 ERA in 16 starts. After the season, he was drafted by the Milwaukee Brewers in the fourth round of the 2016 Major League Baseball draft. Burnes made his professional debut with the Arizona League Brewers and was later promoted to the Wisconsin Timber Rattlers. In 35.2 innings pitched between Arizona and Wisconsin Burnes posted a 3-0 record with a 2.02 ERA. He started the 2017 season with the Carolina Mudcats was later promoted to the Biloxi Shuckers after recording a 1.05 earned run average after ten starts. Burnes finished 2017 with a combined 8-3 record and 1.67 ERA between both teams. The Brewers named him their minor league pitcher of the year after the season. MLB.com ranked Burnes as Milwaukee's second best prospect going into the 2018 season. He began the season with the Colorado Springs Sky Sox. Burnes was called up to the majors for the first time on July 8, 2018 and made his major league debut on July 10, 2018, pitching two scoreless innings, striking out one, and recording his first major league save. In the NLDS against the Rockies, he pitched four scoreless innings in relief across two appearances, earning the win in the clinching 6-0 Game 3 victory. He got the last six outs of NLCS game six win against the Dodgers. To start 2019, it was announced that Burnes would begin the year in the starting rotation. However, he struggled in that role, allowing 11 home runs across his first 3 starts. It was announced he would move back to the bullpen. Things weren’t much better in the bullpen, compiling a 9.00 ERA through 26 appearances. He was placed on the injured list on July 15th with Shoulder Discomfort.