The woman has been identified as a Brooklyn nurse named Ellanora Baidoo. Her husband Victor Sena Blood-Dzraku will be served with the divorce summons via a private Facebook message.
It will be repeated once a week for three consecutive weeks or until "acknowledged" by the man.
According to the Daily News, which reported the story, the couple married in 2009 in a civil ceremony.
The relationship began to unravel when the defendant reneged on his promise to a traditional Ghanaian wedding ceremony, said Ms Baidoo’s lawyer, Andrew Spinnell.
Both spouses are from Ghana.
The ruling says Mr Blood-Dzraku has only been in touch with his wife via phone and Facebook.
The "last address plaintiff has for defendant is an apartment that he vacated in 2011," Judge Cooper said, according to the Daily News.
Ms Baidoo "has spoken with defendant by telephone on occasion and he has told her that he has no fixed address and no place of employment.
"He has also refused to make himself available to be served with divorce papers."
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