Sharif made the remarks during a meeting with visiting German Foreign Minister Guido Westerwelle.
The two leaders discussed bilateral relations and the regional situation.
"Drone attacks are violating our sovereignty as well as international laws. Drone attacks must stop. We have protested many a time. This is simply unacceptable," Sharif was quoted as saying in a statement issued by his office.
Pakistan is "ready to facilitate the withdrawal of coalition troops from Afghanistan and hopes that the Afghan army and security forces would be able to manage the situation" after the drawdown of US and allied forces next year, Sharif said.
Sharif's remarks came hours after US Charge d'Affaires Richard Hoagland was summoned to the Foreign Office to protest a US drone strike in North Waziristan yesterday that killed seven persons.
The protest was lodged on the instructions of the Prime Minister, the Foreign Office said. Former envoy Tariq Fatemi, a Special Assistant to the Prime Minister, handed over a demarche to the US diplomat.
The drone strikes have emerged as a key irritant in Pakistan-US ties.
American officials have defended the use of drones, saying they are vital for targeting Taliban and al-Qaeda elements sheltering in Pakistan's tribal belt.
On May 29, the deputy chief of the banned Tehrik-e-Taliban Pakistan, Waliur Rehman, was killed in another drone strike in North Waziristan.
Sharif spoke out publicly against the drone strikes for the first time shortly after he was formally elected Prime Minister by the lower house of parliament on Wednesday.
He said the attacks should stop as they were a violation of Pakistan's sovereignty.
During his meeting with the German Foreign Minister, Sharif said Pakistan wants to expand cooperation with Afghanistan and support the Afghan nation.
"There had to be a multi-pronged policy to tackle the situation in Afghanistan," he said. Referring to Pakistan's acute energy shortage, Sharif said his government is working on a plan to overcome power outages.
He invited German investors to invest in Pakistan's power sector.
Sharif said Pakistan will welcome German investors to set up thermal power plants to be run on coal and gas. He offered to facilitate the setting up of plants near coal mines.
"We have a tough situation at hand but we have a team and the determination to turn around the economy," Sharif said.
Westerwelle said the German government is keen to send a delegation of 60 businessmen to Pakistan and the German Ambassador will facilitate this visit.
He proposed that a joint investment conference should be held in Pakistan so that investors could share their knowledge and explore prospects of investment.
Westerwelle said Germany would continue to support Pakistan's efforts to get GSP-Plus status in the European Union.