2010-11: Karel Vejmelka played for the Czech second division club SK Horacka Slavia club in his hometown of TrebIc. He had a 2.18 goals against in seven games for the club's U18 team. Vejmelka played 24 games for the SK Horacka Slavia U16 club, posting a 2.41 goals against and .904 save percentage.
2011-12: Vejmelka played at three different levels for SK Horacka Slavia as a 15-year-old and played for the Czech Republic's national team at the U17 and U16 levels. Playing in the Czech U20 second league he had a 2.00 goals against and .852 save percentage in two games. Vejmelka played 17 games in the U18 second division and had a 2.87 goals against and .892 save percentage. Playing 13 games for MD Trebic's U16 team in the top division he had a 5.37 goals against and .885 save percentage. Vejmelka appeared in one game with the Czech U17 team and in eleven games with the Czech U16 team he had a 4.62 goals against and .858 save percentage.
2012-13: Vejmelka moved up to HC Pardubice in the top division — skating for the club's U18 team — and played in five games for the Czech U17 team. He had a 2.60 goals against and .926 save percentage with two shutouts in 17 regular season games and allowed four goals in his only playoff game with HC Pardubice. In five games with the Czech U17 team he had a 5.35 goals against and .848 save percentage.
2013-14: Vejmelka played for HC Pardubice's U20 team and represented the Czech Republic at the U19 and U18 levels. In 34 games for HC Pardubice he had a 2.54 goals against and .933 save percentage with one shutout. Splitting the goaltending duties with Vitek Vanecek at the 2013 World Junior A Challenge, he was 0-2 with a 2.01 goals against and .929 save percentage. In three games with the Czech U18 team prior to the 2014 World Junior Championship he had a 3.33 goals against and .879 save percentage. Vejmelka was ranked 15th amongst International goaltenders in Central Scouting's mid-term rankings prior to the 2014 NHL Draft.
Vejmelka is a big, 6-foot-3 goaltender who tends to profit from his size and uses it well in the net. His saves are not the most acrobatic, but he does a great job of keeping the puck from crossing the goal line by not quitting on a play and getting himself in front of second and third chances.