The three-minute clip, filmed on a hand-held digital camera, features Norwegian troops dancing in fields and military bases as they sing their own version of the dreamy surf song.
The original tune about Kokomo beach in Florida is transformed into a biting satire on international intervention in places such as Kosovo and Rwanda.
"Somalia, Grenada, rescuing Kuwait, we screw ya, Rwanda, wish we could have helped ya, Iraqi embargo ... " they croon, with backing vocals and dance routines performed in combat boots and camouflage gear.
"Down in Kosovo, we'll kick some [expletive] and then we'll see how it goes, and then we really don't know. Good luck to Kosovo.
"Every time we go to little places like Kosovo, we never really know what happens after we go ... It's Europe and Nato, why the hell do we go?"
Nato intervened in Kosovo in 1999 to end former Serbian strongman Slobodan Milosevic's crackdown on the independence-seeking ethnic Albanian majority in the southern province.
Belgrade has never been shy about criticising Nato's interference, which did not have immediate UN approval, and claims to have exposed the Serb minority in Kosovo to revenge attacks by ethnic Albanians.
But the Serbian government was still unable to see the funny side of the Norwegians' parody, particularly the jabs at "Serbian bad guys" and references to Belgrade's past oppression of the Kosovo Albanians.
Slobodan Milosevic (R) is also
ridiculed in the song
Fully armed and patrolling deserted Kosovo back roads, the Norwegians sing "protecting human rights, air strikes and fire fights, and we'll be dropping bombs wherever Serbian bad guys hide ... just up from Kosovo (in Serbia)".
"Somewhere far overseas, there's a place called Kosovo, that's where you don't want to go if you're Albanian at all... Milosevic, you son of a [expletive]."
Serbian television stations broadcast the video clip and it quickly became an internet hit throughout the Balkans, sparking a row between Belgrade and Oslo, and forcing Norwegian ambassador Hans Ola Urstad to formally apologise.
"I really hope this incident will not disturb the lasting and deep friendly relations between our countries," he said on Tuesday, promising to launch an official investigation into the song.
Slobodan Samardzic, an adviser to the Serbian prime minister, said the song was proof that the Nato mission in Kosovo (KFOR) was an abysmal failure.
"Such things only help the Serbian side to prove that there is no security in Kosovo, no respect for human rights and no multi-ethnicity," he said.
The North Atlantic Treaty Organisation has about 17,000 troops in Kosovo, more than any other deployment including Afghanistan.
They are supposed to be keeping peace between the ethnic Albanian majority, which wants independence, and the ethnic Serb minority, which wants to stay with Serbia.
But the alliance is regularly accused of failing to protect the Serbs, who claim to be living in constant fear of attack by Albanians. Scores of thousands of Kosovo Serbs are refugees, too scared to return.
Last year KFOR failed to stop mobs of ethnic Albanians from rampaging through supposedly protected Serb enclaves for three days.
"The clip shows that international soldiers in Kosovo are not machines but humans with feelings and opinions about reality. I don't find the clip offensive but instructive"
Kosovo Albanian art editor
One Nato commander described the violence, the worst since the 1998-1999 conflict, as an organised campaign of "ethnic cleansing" - exactly what the alliance intervened to stop.
KFOR headquarters in Kosovo was stung by the joke, describing the Norwegians' song as a "stupid and unacceptable private initiative of some soldiers".
"The behaviour of the singers and the words of the song are unworthy of Nato and KFOR," the command said in a statement.
"Their inadmissible joke must not hide the high level of professionalism and impartiality of the 17,000 soldiers of KFOR, who currently and every single day work to implement a safe and secure environment in Kosovo."
While Belgrade fumed and Nato squirmed, Kosovo Albanians seemed to share the Norwegians' irreverent take on the situation.
"The clip shows that international soldiers in Kosovo are not machines but humans with feelings and opinions about reality. I don't find the clip offensive but instructive," Kosovo Albanian art editor Arif Muharremi said.