"Jeg har skjorte på."
Translation:I wear a shirt.
The Tips and Notes state:
One more thing to note is that in Danish it is possible to omit the article before the thing you’re wearing. For instance:
• Jeg har en kjole på → literally I have a dress on meaning I am wearing a dress
• Jeg har kjole på → literally I have dress on meaning I am wearing a dress
Both options are correct, though, so don’t worry. ;) Most often the second one (without article) is used, while the first one is chosen if one wishes to add emphasis to the item being worn.