Health insurance 

Most commercial pension plans have a health insurance part: Almost all of them covers osteopathy. Usually they cover a number of treatments and part of the cost.  pension companies like : 

PFA

Danica Sundshedsforsikring

Nordea sundhedsforsikring

Dansk Sundhedsforsikring

LB

Tryg

Codan

and many more. 

By injury or accident your insurance also very often covers osteopathic treatment. 

Sygeforsikringen Danmark also covers group 1,2 and 5

The common health insurance in Denmark is not covering osteopathy