It is the first time sitting members have been asked to give such details.
The public register, to be issued this autumn, will log if a judge refuses to answer and will be extended to cover sitting magistrates later in the year.
The government has already made declaration of any Masonic membership a condition of appointment for new judges, magistrates, police, prison and probation officers.
The request follows repeated refusals by the United Grand Lodge to hand over details of its members to the government.
It has said that it will campaign to keep the identity of its members a secret.
Tackling 'public concern'
In a letter to the Lord Chief Justice, Lord Bingham of Cornhill, Lord Irvine expressed his confidence in the integrity of the judiciary but said public concern could undermine confidence in the justice system.
He said: "I believe that any substantial 'non-co-operation' could create a suspicion in the minds of the public and weaken confidence in the judiciary.
"I suspect that a full set of responses will also serve to demonstrate that Masonic membership among the judiciary is nothing like as great as some people suppose."
A spokesman for the United Grand Lodge John Hamill said: "We regret that the Lord Chancellor has found it necessary to do this, particularly as it's based, as he says, on a perception for which there's no evidence.
"We would certainly question, as we have done from the first, why Freemasons are being singled out from all other associations that people can belong to."
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