Morten Wieghorst, who was assistant manager to Hjulmand from 2020 and also formerly head coach of Denmark's under-21 side, will take over as interim national coach until 2025.
After four years at the helm, Hjulmand said the team needed new energy and had asked for his contract, valid for another year, to be cancelled, the association said.
The Danes have been winless in their last seven games in a row at major tournaments - the 2022 World Cup and the 2024 European Championship - scoring only three goals.
A 2-0 defeat by hosts Germany in the last-16 saw Denmark exit the Euros with a lack of attacking power blamed for blunting their chances at major tournaments.
"I have given everything I had to achieve success and to get the people to rally around the team. Representing one's country is absolutely the greatest thing I can imagine," the coach said in a statement.
"When I look two years ahead to the World Cup 2026, I feel that it will be best for the team that a new face with new ideas comes in, who can write a new big chapter for this amazing team.
"Therefore it is best that someone else leads the team forward. It's not about me. It's about what's best for the team."
Hjulmand guided Denmark to the semi-final of Euro 2020 and was credited for their impressive run in the 2024 qualifiers.
The Danes finished bottom of their group at the Qatar World Cup despite being first in their qualifying group.