The move comes two days after Sharif, who also holds foreign affairs portfolio, called for an end to the campaign by the CIA-operated spy planes.
"The US Charge d' Affaires, Ambassador Richard Hoagland, was summoned this afternoon to the Foreign Office by Special Assistant to the Prime Minister and Minister of State for Foreign Affairs, Mr Tariq Fatemi to lodge a strong protest on the US drone strike carried out in North Waziristan on June 7, 2013," said a statement from the Foreign Office spokesman.
Former envoy Tariq Fatemi, a Special Assistant to the Prime Minister, handed over a demarche to the US diplomat.
Hoagland was told by Fatemi that the government strongly condemns the drone strikes as a "violation of Pakistan's sovereignty and territorial integrity".
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The statement further said: "The importance of bringing an immediate end to drone strikes was emphasized."
Fatemi pointed out that the Pakistan government has consistently maintained that drone strikes are "counter-productive, entail loss of innocent civilian lives and have human rights and humanitarian implications".
The drone strikes also "have a negative impact on the mutual desire of both countries to forge a cordial and cooperative relationship and to ensure peace and stability in the region", the statement said.
TV news channels reported that a "high value target" was among those killed.
On May 29, the deputy chief of the banned Tehrik-e-Taliban Pakistan, Waliur Rehman, was killed in another drone strike in North Waziristan.
Shortly after being formally elected Prime Minister by the lower house of parliament on Wednesday, Sharif said that the attacks by US drones in Pakistan's tribal belt should stop.
He described the attacks as a violation of the country's sovereignty.