[2][3] After starting his career as a talent of Herfølge and later English Championship club Charlton Athletic, Rygaard played multiple season in the lower divisions of Danish football.

Most notable was his stint at Næstved, where he made 155 appearances and scored 38 competitive goals which earned him a "Player of the Year" Award of the Danish 2nd Divisions in 2014.

After progressing through the youth ranks, he was invited for a trial at English Championship club Charlton Athletic after they had previously signed fellow Herfølge-talent, Martin Christensen.

[6] On 3 December 2009, Rygaard was notified by general manager, Per Rud, and head coach, Auri, that his contract, running to July 2010, would not be extended and that they would listen to offers from other clubs during the winter transfer window.

[10] After scoring 13 goals in 12 appearances for B.1921 he was signed on a two-year deal by his first youth club, now called Lolland Falster Alliancen, who played in the Danish 2nd Divisions.

At Lyngby, he made his European debut in the first qualifying round of the 2017–18 UEFA Europa League at home against Welsh club Bangor City, starting in midfield before being substituted at halftime.

[17] After knocking out the club 4–0 on aggregate, Lyngby defeated Slovak side Slovan Bratislava in the second round, with Rygaard scoring in the return leg on a penalty – his first European goal.

[19] During a tumultuous 2017–18 Superliga campaign, where Lyngby fought relegation and their financial situation worsened,[20][21] Rygaard left the club after not receiving his salary for seven days in February.

[38] He established himself as a consistent performer, and by the end of the season, he had played for BK Häcken 31 times in all competitions, scoring 11 goals and providing four assists,[39] helping them to their first ever Allsvenskan title.