2008-09: Selected by Victoriaville in the first round (8th overall) of the 2008 CHL Import Draft, Andrej Nestrasil skated for the QMJHL’s Tigres in his first season in North America and represented the Czech Republic at the 2009 U18 World Junior Championships. Nestrasil was the second-leading scorer for the Tigres with 22 goals and 35 assists in 66 games and was minus-two with 67 penalty minutes. Victoriaville reached the playoffs after finishing third in the Central Division. Nestrasil scored 2 goals with 1 assist and was minus-two with 10 penalty minutes in the four game series with Shawinigan. In six games for the sixth-place Czech Republic squad at the U18 WJC he scored 2 goals with 2 assists and was an even plus/minus with 6 penalty minutes. Ranked 131st amongst North American skaters in Central Scouting’s final rankings, he was selected by Detroit in the third round (75th overall) of the 2009 NHL Draft.
2009-10: Nestrasil got off to a fast start for Victoriaville in his second season but his production slipped in the latter part of the season. Due to both a nagging injury late in January and the addition of five new forwards acquired by the Tigres in mid-season trades he was limited late in the year; when the Tigres made a run to the QMJHL semifinals. Nestrasil had 43 points in the Tigres’ first 44 games and finished with 16 goals and 35 assists with a plus-four plus/minus and 40 penalty minutes in 50 regular season games. In 16 playoff games he was minus-two with 2 goals, 4 assists and 10 penally minutes. Nestrasil skated for the Czech Republic at the 2010 U20 World Junior Championship. In six games he scored 1 goal with 6 assists and was minus-2 with 4 penalty minutes. The Czech Republic missed the quarterfinals – finishing seventh.
2010-11: Acquired by Prince Edward Island in an off-season trade, Nestrasil was the second-leading scorer for the Rocket and represented the Czech Republic at the 2011 U20 World Junior Championship . He scored 19 goals with 51 assists and was plus-13 with 40 penalty minutes despite missing eight games in his third QMJHL season. Prince Edward Island reached the playoffs after finishing fourth in the Maritimes Division. Nestrasil scored 1 goal with 5 assists and was plus-three with 2 penalty minutes in the six-game playoff series with Shawinigan. Playing for a Czech Republic squad that finished seventh for the second straight year at the WJC, he was minus-five with 1 goal and 2 assists.
2011-12: Nestrasil split his first pro season between the Red Wings’ AHL and ECHL affiliates in Grand Rapids and Toledo. He opened the season with Toledo, was re-called by the Griffins and, after playing 11 games was sent back to Toledo; returning to Grand Rapids in late March. Nestrasil scored 3 goals with 1 assist and was minus-four with 6 penalty minutes in 25 games for the Griffins. In 51 ECHL games with the Walleye he scored 7 goals with 22 assists and was minus-ten with 20 penalty minutes. He did not see any playoff action as neither Grand Rapids nor Toledo made the playoffs in their respective leagues.
2012-13: Nestrasil appeared in 25 regular season games and one playoff contest for Detroit AHL affiliate Grand Rapids in his second pro season — spending most of the year with the ECHL’s Toledo Walleye. He appeared in three December games and three January contests before joining Grand Rapids for an extended stay in the middle of February. Nestrasil scored 3 goals with 3 assists and was +1 with 2 penalty minutes during the regular season. The Griffins finished first in the Midwest Division and captured the Calder Cup championship. Nestrasil made his only playoff appearance in Game 3 of the Western Conference finals — finishing -2 with no points nor penalty minutes in the Griffins’ 4-1 loss to Oklahoma City. Nestrasil was a point-per-game scorer with Toledo. He scored 11 goals with 30 assists and was +17 with 26 penalty minutes in 40 regular season games and had 1 goal and 2 assists, finishing -3, in four ECHL playoff games.
Nestrasil's ability to make plays at high speed allows him to surprise his opponents and catch opposing defensemen flat-footed. At 6'3 and 206lbs pounds, Nestrasil has decent size, but he still has some work to do in adapting to the physical style in North America and playing a more complete game.
Nestrasil was placed on waivers by Detroit and claimed by the Carolina Hurricanes in November of 2014.