They made their plea in an interfaith statement, released in Marrakesh on the sidelines of UN talks tasked with implementing a landmark climate treaty.
Signatories also included Marcelo Sanchez Sorondo, Chancellor of the Pontifical Academy of Sciences; Olav Fykse Tveit, head of the World Council of Churches; and more than 200 other faith leaders.
National and private investment funds have placed trillions of dollars in fossil fuel energy and related sectors.
The Paris Agreement, seeks to beat back the threat of global warming, caused mainly by the burning of coal, oil and gas.
The 196-nation pact calls for the rapid decarbonisation of the world economy -- essentially a switch from carbon-intensive to clean energy, especially solar and wind.
The appeal was led by a pledge from the Islamic Society of North America, an umbrella group, to divest from fossil fuels and encourage sister organisations to do the same.