Enjoyed a prolific amateur career, triumphing at the 2018 Eisenhower Trophy for Denmark alongside identical twin brother Nicolai and John Axelsen. The twin duo also represented Europe at The 2018 Junior Ryder Cup.

Secured his card for the 2020 season at Qualifying School Final Stage, becoming the first player born in the 21st century to graduate from the Qualifying School. At 18 years and 271 days old, he became the third youngest winner in DP World Tour history with a dramatic play-off triumph at the AfrAsia Bank Mauritius Open in just his fifth start.

The victory made him the fastest Dane to a DP World Tour title, beating 15-time DP World Tour winner Thomas Bjørn's record of 24 events.

He then became the second-youngest player in Tour history to record multiple wins after securing his second title at the 2020 ISPS Handa UK Championship, defeating Justin Walters in a play-off at the age of 19 years and 171 days.

Højgaard won his third title at the age of just 20, winning the 2021 Omega European Masters, carding a final round 63 to claim a one stroke victory. The win contributed to an historic double on the DP World Tour, as his brother Nicolai was victorious the following week at the DS Automobiles Italian Open.

Became the first home winner of Made in HimmerLand in 2023 after a six-hole play-off against Nacho Elvira in the tournament’s last ever staging at the Danish venue. Came from seven shots behind to force a play-off with the Spaniard and then improved his record in DP World Tour play-offs to three wins from three.

Held off Rory McIlroy to win his fifth DP World Tour title at the 2024 Amgen Irish Open at Royal County Down. Finished a career-high second on the 2024 Race to Dubai Rankings, earning dual membership on the PGA TOUR for 2025, just 12 months after missing out on one of the ten cards for the previous season by one place.

Represented Continental Europe at the 2025 Team Cup.