Denmark were unseeded and could therefore draw the world's strongest tennis nations.
For the same reason, the Danish Davis Cup captain, Frederik Lochte Nielsen, believes that the draw "could have been worse".
"It is a match where I think our players can assert themselves, and we have a chance", he says in a press release from the Danish Tennis Association.
"I think we have some possibilities. When you are unseeded, all matches are tough, of course. But it could have been worse", says Frederik Løchte Nielsen.
Croatia's highest-ranked player is Marin Cilic, who is ranked 75th in the world. Borna Coric is number 115 in the world.
Denmark's last meeting with Croatia dates back to 1993, when the Danes won 3-2.
The match against the Croatians will be played between 6 and 9 February in Croatia next year.
The Davis Cup match is decided by the best of five matches. Two singles are played on the first day, and a doubles match is followed by two singles on the second day.
If Denmark advances to the second round of qualification, either Germany or Peru awaits.