"Over the summer we became suspicious after receiving information from a foreign authority," said Jesper Ronnow Simonsen, head of the Skat tax agency.
"Our own internal investigations have strengthened our suspicions and we have therefore turned the case over to the police," he said in a statement.
Danish police confirmed the investigation, saying the case -- which involves a sum of 6.2 billion kroner ($918 million) -- was top priority.
A Skat spokesman was not willing to disclose which country had flagged up the matter to Denmark.
The case involves returns on stock, including dividends, in Danish companies paid to foreign companies.
Dividends normally carry a 27 percent tax in Denmark. Under double taxation agreements, however, foreign companies based abroad are entitled to a refund of part or all of the Danish tax, if they have paid tax on the dividend in their country of domicile.
Simonsen said Skat's investigations showed that "a large network of companies abroad have apparently applied to have their dividend taxes refunded for fictional share holdings, based on falsified documents."
"The expected criminal fraud in refunds has so far been calculated based on 2,120 individual claims totalling some 6.2 billion kroner in the 2012 to 2015 period," Skat said.
The Danish police's Special Economic and International Crime unit (SOIK) said the case was a top priority.
"The treasury and society have possibly been robbed of very considerable funds... We have a major investigation ahead of us. I envisage a long hard haul to find out what has happened," National Prosecutor Morten Niels Jacobsen said in a statement.
Neither the tax authority nor the SOIK would disclose any information on the cases, or name any of the companies involved.