Unfortunately, no. There is no direct ferry service between Denmark and Finland at all. From the Danish capital, you can go to Oslo, the capital of Norway, and transfer to the Swedish port of Ystad to the Polish port of Swinoujscie, without transplantations.

So if you really want to do some of the way from Helsinki to Copenhagen by ferry, it makes sense to get to Sweden. First on a direct ferry to Stockholm, and from the Swedish capital to the destination by bus or train (then a transfer to Malmö is added).

The second route: ferries from Helsinki to Travemünde, Germany, then by Travemünde-Malmö ferry, Sweden, and from there bus, rental car or train to Copenhagen