Nationalbanken reduced its deposit rate, which was cut to below zero in September for the first time since 2012, to -0.2 percent from -0.05 percent on Monday.
The lending rate was lowered to 0.05 percent from 0.2 percent.
"The interest rate in Denmark is now the same as in the eurozone. This will take the pressure off the krone," Nordea economist Helge Pedersen wrote on Twitter.
The move came as analysts expected that the European Central Bank will unveil a vast bond-buying programme this week aimed at kickstarting growth, which has put pressure on the euro.
"The central bank is reacting to the strong krone. Probably not the last cut," Danske Bank economist Steen Bocian wrote.
On Thursday, the Swiss National Bank (SNB) removed the cap of 1.20 francs to the European single currency, prompting the Swiss franc to surge 30 percent against the euro minutes after the announcement.
Denmark's monetary policy is aimed at maintaining a stable exchange rate between the Danish krone and the euro.
The krone is pegged to the euro through an agreement known as the European Exchange Rate Mechanism (ERM II), under which the Danish currency can move only 2.25 percent up or down from a fixed rate of 7.46 krone per euro.
The deposit rate is the rate at which commercial banks are paid, or in this case have to pay, to place funds at the central bank.