"Terrorists are likely to try to carry out attacks in Denmark. Attacks could be indiscriminate, including in places frequented by foreigners," the office said in an updated travel advice.
The office added that Denmark had successfully "disrupted a number of planned attacks and made a number of arrests."
"There is a high threat of terrorist attack globally affecting UK interests and British nationals, including from groups and individuals who view the UK and British nationals as targets," the office said, urging nationals to remain "vigilant at all times."
On Sunday, the UK foreign office also warned of a growing terrorist threat in Sweden.
Last week, Swedish police's chief of counterterrorism, Magnus Sjoberg, said that Sweden, along with Denmark and the Netherlands, has become a target of terrorist groups after it allowed demonstrations in its territory involving the burning of the Quran.
Several Quran-burning demonstrations have taken place in Denmark and Sweden in recent months. Most Muslim countries have condemned the demonstrations, and some have summoned the Swedish and Danish ambassadors to issue letters of protest.