The organisation has written to the abbey's dean to say the ceremony - hosted by the Royal Navy - would undermine the Church of England's (C of E) opposition to nuclear weapons.
In a letter to Very Rev John Hall, Paul Parker from Quakers in Britain, which has 22,400 attendees, said: "Quakers regard nuclear weapons as faithless.
"To threaten humanity and the planet with nuclear annihilation is in our view contrary to what God would have us do.
"It is indeed imperative that we all continue to pray and work for peace throughout the world, but peace is not served by the maintenance, possession and threat of use of nuclear weapons."
Last summer, the C of E's governing body passed a motion which said Christians ought to "work tirelessly" for the elimination of nuclear weapons.
Premier reported last month on how the Christian Campaign for Nuclear Disarmament urged Westminster Abbey to think again about hosting the service - planned for 3rd May.
"Peace is not served by the maintenance, possession and threat of use of nuclear weapons."@RCquaker criticises Westminster Abbey's 'National Service of Thanksgiving to mark 50 years of the Continuous at Sea Deterrent' https://t.co/na0WFip0gp
— Quakers in Britain (@BritishQuakers) April 9, 2019
But the abbey refuted claims the ceremony was service of thanksgiving or celebration for nuclear weapons.
A spokesman told Premier: "The service will recognise the commitment of the Royal Navy to effective peace-keeping through the deterrent over the past fifty years and will pray for peace throughout the world."
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