Messaging in English on its official Twitter account, the government said that half an hour after midnight (1130 GMT), "An unknown person committed suicide with an explosive device", presstv.ir reported.
It added, "Immediately before, that person threw an explosive device from the intersection near the Sport Center into the US embassy compound."
It said, "Most probably, the device was a hand grenade," adding that police investigation and identification were underway.
A Reuters photographer in Podgorica said a police vehicle blocked the street where the embassy is located, adding that no damage was visible.
The embassy warned US citizens to stay away until further notice.
"The US embassy in Podgorica advises US citizens there is an active security situation at the US embassy in Podgorica," it said on its website. "Avoid the embassy until further notice."
Earlier, media in Montenegro had said the attack occurred minutes before midnight.
Montenegro, the smallest of all former Yugoslav republics, was the 29th country to join NATO last May.