The ministry said that since being informed of the man's disappearance on 11 April, it had been in talks with a Sunni Muslim cleric, US-occupation forces and local authorities in order to find him.
"There is as yet no information about the perpetrators or a motive for the killing," the ministry said in a statement on Wednesday.
"The ministry was informed last night by the Coalition Provisional Authority that a Danish citizen had been found by the Iraqi police. The time of death was not revealed," it said.
On 16 April, the ministry officially confirmed that a Danish citizen was missing. It did not name him but local media have identified him as 35-year-old Henrik Frandsen.
According to Danish media, the man, visiting Iraq to set up a sewerage business, was kidnapped during a highway robbery in the town of Taji outside Baghdad.
Denmark supported the US-led invasion of Iraq and now has around 500 troops in the country.
The European Union condemned the killing and urged kidnappers in Iraq to release their hostages unharmed.
"I condemn utterly the murder of this man and extend my condolences to his family and friends," said Irish Foreign Minister Brian Cowen, speaking on behalf of the EU presidency.
"I call on those responsible for hostage-taking in Iraq to release immediately and unharmed all hostages and to desist from this deplorable activity," Cowen said in a statement.
Some 50 foreigners have been abducted during a recent spate of violence in Iraq.