Ellemann-Jensen was on sick leave last week after feeling nauseous and faint.
“I’ve always been the type to do my job, so I was set on coming back right away. But now that a few days have passed, I realize I’m not ready,” he writes.
Prime Minister Mette Frederiksen (S) says she supports him in the decision.
“His body has sent clear signals, and that should be taken seriously,” she writes on Facebook and continues: “You can’t be both father, defense minister and party leader if you don’t feel well.”
Elleman-Jensen is replaced in the government by Economy Minister Troels Lund Poulsen, also from Venstre, and as party leader by Deputy Chairwoman Stephanie Lose.