The condemnation came as pro-government dailies saw sending the vessel as a clear signal to Syria, which is being blamed by the ruling majority for blocking a presidential vote in Beirut.
"This decision proves that it's the United States which is interfering in Lebanese affairs, and that this interference has taken on a military slant," Hezbollah MP Hussein Hajj Hassan told AFP.
The United States said on Thursday it had sent the guided-missile destroyer to the waters off Lebanon, which has been embroiled in a paralysing political crisis for months.
The USS Cole was the target of a bombing by Al-Qaeda extremists in October 2000 in the Yemeni port of Aden that killed 17 US sailors.
It is "a show of support for regional stability" because of "concern about the situation in Lebanon," a US official said on condition of anonymity, declining to say that the show of force was meant for Syria or Iran.
Prime Minister Fuad Siniora, whose government is backed by the West and most Arab countries, stressed during a meeting with Arab ambassadors that Beirut did not ask for the warship and summoned a top US diplomat for "clarifications."
"We did not ask anyone to send warships," Siniora said, adding that no US warship was in "Lebanese waters."
Earlier Siniora summoned US charge d'affaires Michele Sison "to ask her to clarify the presence of the USS Cole" in the Mediterranean, a government source told AFP.
"Mrs Sison assured him that the warship was in international waters and had been dispatched to guarantee regional stability," the source added.
The United States, meanwhile, shrugged off Hezbollah's criticism.
"On Hezbollah's concerns, I would express some of our own concerns with Hezbollah's actions. So I'll just leave it at that," White House national security spokesman Gordon Johndroe told reporters.
Johndroe sidestepped questions about the comments from Siniora.
"We have regular consultations with Prime Minister Siniora and his government, as well as our allies, both in the immediate region, as well as in Europe on the situation in Lebanon," said the spokesman.
Lebanon has been without a president since last November amid political feuding between the ruling parliamentary majority and the opposition, backed by Syria and Iran.
The majority accuses Syria of blocking efforts to elect a new president in Lebanon, which was under Syrian military domination for 29 years until Damascus withdrew its troops in April 2005.
Fears of civil strife in Lebanon have mounted over the continued deadlock and warnings of wider conflict after the February 12 assassination in Syria of top Hezbollah commander Imad Mughnieh.
Hezbollah chief Hassan Nasrallah mourned Mughnieh in a massive public rally, threatening "open war" against Israel, which fought a devastating July-August 2006 war against the Shiite group.
"Wars begin by an exchange of messages. The American decision is the first message to its opponents in the region saying 'we are here'," said Wehbe Katisha, a retired Lebanese army general.
Beirut has also been the scene of recent street clashes between supporters of the rival factions, prompting several Gulf nations and Western states to advise their citizens against travelling to Lebanon.
Also on Friday, Germany handed over command of the maritime unit of a UN peacekeeping force to Italy, the United Nations Interim Force in Lebanon said.
It said German Defence Minister Franz Josef Jung, UNIFIL commander Claudio Graziano, Italy's ambassador to Lebanon, Gabriele Checchia, took part in a handover ceremony on a German vessel off Beirut port.
The mission of the multinational maritime unit, set up after the Israel-Hezbollah war, is to curb arms smuggling.
