It warned that Westboro's websites would be attacked if the congregation did not stop its public protests.
In a defiant response, the church said it would not be silenced, and urged Anonymous to "bring it".
Westboro Baptist Church has been widely condemned for its aggressive anti-gay campaigning.
A number of US states have passed legislation, banning Westboro's members from protesting close to military funerals.
The church's leader, pastor Fred Phelps, was banned from entering the UK by the Home Office in 2009.
Activist hackers Anonymous is known for its "hacktivism", targeting individuals, companies and governments whose behavior it objects to.
The group recently crashed a number of Egyptian government websites, in support of the country's pro-democracy protests.
It also attacked several online companies that it believed had helped clamp down on Wikileaks' activity, including Paypal and Amazon.
Despite being posted on an Anonymous news site, there was some uncertainty surrounding the provenance of the letter.
Further messages on the same website questioned its authenticity.
The confusion is understandable, according to Graham Cluley from security firm Sophos.
"Anonymous is a headless organisation," he said.
Mr Cluley warned that its followers could potentially be led into mounting a major hack under false pretenses.
"There are dangers in future that someone may pose as Anonymous and say that they want an attack".
The Westboro Baptist Church issued a statement, branding Anonymous "a puddle of pimple-faced nerds".
It called the threat a "bad miscalculation", and appeared to goad Anonymous to action, with the phrase "bring it!".
The church's website, godhatesfags.com was unavailable.
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