In a debate at its annual Conference in Plymouth, the Church called upon the Government to urge the US to discontinue the practice.
In a report on drone warfare presented to the Conference, policy experts note that in the wake of 9/11, the CIA has carried out a "persistent campaign" of targeted killings using unmanned aircraft in northern Pakistan.
"Accurate figures for those killed are difficult to obtain but estimates suggest between 1,717 and 2,680 since 2004," the report states.
"It is even more difficult to determine what proportion of those persons killed were militants, terrorists or civilians.
"Terrorists are not warriors and those suspected to be guilty of, or to be plotting, even the most dreadful of crimes need to be dealt with using an accountable judicial process."
The Church is concerned that a reliance on drones and other remotely operated weaponry will lead to an increase in armed intervention as the physical risk to troops is lowered.
It wants to see the UK Government publish more information about its military strategy, particularly in relation to counter insurgency.
Steve Hucklesby, a Methodist policy adviser and member of the working group, said: "If there is a legitimate use for this technology we need a much clearer idea of the boundaries for its use.
"Terrorists function outside the law. It is vitally important that the UK and its allies do not do so as well.
"The targeted killings carried out by the CIA in northern Pakistan demonstrate only too clearly the ethical challenges that will face us as this technology proliferates more widely."
The Methodist Church's conclusions have drawn support from the United Reformed Church (URC) and the Baptist Union of Great Britain (BUGB).
The URC is a member of the Joint Public Issues Team that submitted the report debated at Methodist Conference
Frank Kantor, the URC's Secretary for Church and Society, said the URC would be grappling with the same issue at its General Assembly this week.
"The ethical and moral issues surrounding drones are a significant issue and we are pleased that the Methodist Conference has engaged with this debate," he said.
Stephen Keyworth, Head of Faith and Unity at the BUGB, said: "Drone technology and its use in conflict present us with a new dimension to an age-old ethical issue.
"We welcome the work completed for the report and the way it has been addressed by the Methodist Conference.
"Baptists will have an opportunity to make a similar contribution to this important debate in the coming months."