Amid a low-growth environment, a significant output gap, indebted households and concerns over the impact of negative rates on the housing market, Denmark is already facing an uncertain future without Brexit.
"(The fall in sterling) is affecting the Danish economy already," Jan Størup Nielsen, chief analyst, at Nordea Bank told CNBC on Friday.
Before the Brexit vote, the pound was nearly 9.8 Danish crown, or krone. That has now dropped to about 8.27 crowns.
"The significant weakening of the pound against the Danish krona is hurting exports, including on agricultural products," Nielsen added.
According to Nordea, Danish exports to the U.K. dropped nearly 0.5 billion Danish crowns ($0.07 billion) since the June vote. It is now at 2.75 billion DKK ($0.04 billion).
The Danish economy is gradually recovering from the 2008 financial crisis, but investment and exports are two of the main issues that the government needs to fix.
The fund warned: "A sharper than expected slowdown in Europe or in emerging markets could derail the modest recovery, given Denmark's deep integration in the world economy."
"The disruption of trade and financial flows that are likely to accompany a Brexit would compound these risks," the IMF added.
Claus Hjort Frederiksen, Denmark's finance minister, highlighted in early October worries over trade policy. "Trade-friendly policies aimed at reviving confidence and raising productivity are needed," he said.
"The prospect of the UK leaving the EU adds another major source of economic uncertainty. In negotiating the future relations between the U.K. and the EU, as well as with other partners, all efforts should be made to minimize this uncertainty and to ensure continued close economic ties," Frederiksen said.
Other analysts expect the impact to be marginal over the short term, but the falling sterling is a longer-term concern for Danish exporters.
"We expect Brexit to have only a marginal impact on the Danish economy in the short term. There is nothing much to suggest a sharp deceleration of the UK economy presently, but the decline in sterling is likely to cause a margin compression for Danish exporters to the British market," Teis Knuthsen, chief investment officer at Saxo Private Bank told CNBC via email.
"It remains to be seen whether a British exit from the EU will cause a deterioration of bilateral trade flows that are not compensated by increased trade with other countries. However, the timing of that extends beyond 2019, as the U.K. will only trigger the two-year article 50 negotiation program in 2017," he added.
Denmark, like many other European countries, has to deal with a rising support for populist movements. The Danish People's party, which opposes the country's EU membership, obtained 15 new seats at the last general election and is the second largest in parliament.
Such political and economic landscape, could make the Danish government take a tougher stance in the upcoming Brexit negotiations. Lars Rasmussen, the Danish prime minister said, the Brexit vote was "tragic", but he wants a "friendly divorce", the Wall Street Journal reported.