Reporter Stefan Weichert and photographer Emil Filtenborg Mikkelsen “were rapidly taken to hospital and are out of danger”, the Danish newspaper Ekstra Bladet said.
The two had been reporting near the northeastern city of Okhtyrka, some 50 kilometres (30 miles) from the Russian border, it said.
They were wounded despite wearing bullet-proof vests.
The newspaper, which was employing them both as stringers, said it was in touch with Denmark’s foreign ministry and a private company to evacuate them.
Saturday marked the third day since Russian leader Vladimir Putin unleashed a full-scale invasion of Ukraine that has killed dozens of people, forced more than 50,000 to flee the country in just 48 hours and sparked fears of a wider conflict in Europe.