The man's body was found 100 feet from the embassy's wall, according to Steve Goldstein, US undersecretary of state for public diplomacy and public affairs.
The U.S. State Department says it doesn't believe that an attack on the American embassy in Montenegro "is part of an ongoing threat".
Jaukovic, born in the southern city of Kraljevo, Serbia, and residing in Podgorica, launched a hand grenade to the US diplomatic mission early yesterday and then killed himself by activating another explosive device.
Montenegro is located in southeastern Europe and was once part of Yugoslavia.
Montenegro's main daily paper Vijesti identified the attacker as a 43-year-old man born in neighbouring Serbia but who was living in Podgorica.
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Police sources said Janukovic had Montenegrin citizenship and no criminal record. "Immediately before, the person threw an explosive device from the intersection near the Sport Center into the US Embassy compound", read a tweet on the government's official Twitter account. Friends of his family said they were uncertain what might have motivated him to bomb the embassy.
No one else apparently was hurt and there was no major damage.
The news site Portalanalitika.me cited witnesses as saying that police arrived quickly on the scene and sealed off the nearby Boulevard of the Revolution, close to the embassy.
Many in Montenegro remain opposed to the country's membership in North Atlantic Treaty Organisation because of the air war the alliance waged to stop the war in Kosovo when Montenegro was still part of Yugoslavia.