Hojbjerg will lead the Danes tonight against the Faroe Islands.
He said: "It's big for me and a huge pat on the back.
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"After one of the first international matches I had played, Morten Olsen grabbed me and said I had the personality and potential to become national team captain.
"Here it happens after 75 games. And I am incredibly grateful and proud of that.
"It is important to be yourself. I know that my role obliges, and I am also ready to take responsibility.
"It is a milestone for me. I'm not usually the type who looks back so much, but looks forward more."