I go into the initial reception and publication history of the Manifesto here.

One important context is this promised Danish translation never materialized (though a Swedish translation was perhaps one of the first). Another is that there couldn’t be a strong communist Danish contingent because communism didn’t really exist at this point. I don’t know how strong socialism was in Denmark during this period, but I imagine it was relatively secure, as Denmark was a very politically liberal country in this period, for instance achieving universal male suffrage shortly after the Manifesto came out, which is before almost any other country in Western Europe. This was also a high point of Danish intellectual activity—for instance, both Hans Christian Andersen and Søren Kierkegaard were active in 1847.

As a practical point, German-Danish bilingualism was high. This was in part because German was the prestige language in Denmark (most of Kiekegaard’s post enlightenment influences are German; for instance, in 1841, he attended the same lecture series given by Schilling at the University of Berlin that Mikhail Bakunin and Friedrich Engels also coincidentally attended). This was also the period when Germany nationalism and Danish nationalism were starting to clash over Schleswig-Holstein (the Manifesto was published in 1847, war broke out in 1848). Considering that the Manifesto was written by German political exiles in England, I imagine that bilingualism had an influence, though I’m not sure how directly (whether there were Danish political exiles in the League of Just/Communist League, I don’t know).

I don’t know if there is a definitive answer, but I imagine it’s hard to say because, as I mentioned here and detail in my long post, most of those promised translations (including the Danish) didn’t actually come out for about 20-25 years. I think a French translation didn’t even come out until 1872. The text was far from quickly influential. Engels apparently said a Danish edition came out around 1863-1867 but this is something he seems to have organized himself and it’s unclear exactly when or where this came out.