"The court returned a civil judgment, but marriage is a religious act," said the 86-year-old leader, whose community accounts for about 10 percent of Egypt's 80-million largely Muslim population and is the Middle East's biggest Christian society.
Several hundred Copts demonstrated against the ruling in Cairo on Wednesday, gathering before the capital's St Mark's Cathedral.
They carried placards exclaiming "'no' to remarriage; we follow the teachings of the Bible" or "we are all behind our holy patriarch in rejecting a judgement that runs counter to Christian precepts."
The ruling related to the case of Hani Wasfi, who complained against the pope's refusal to let him remarry after divorce.
Copts forbid divorce or remarriage except in proven cases of adultery, or if a spouse converts to another religion or branch of Christianity.
Civil marriage alone, without a religious ceremony, is not recognised in Egypt, where Muslims are allowed to remarry.
The remarriage debate, launched by secular or divorced Copts and civil rights organisations, is caught up in religious tensions and the rise of religious fundamentalism.
"Apart from divorcees, the other Copts think this is a battle against them and support Shenuda," says Karima Kamal, who has written about divorce among the Copts.
"The debate is held hostage to the growing religious radicalisation in Egypt," she says.
Some Copts do feel persecuted or marginalised by the state.
"Why can't we build churches freely?" cries Guebrail, who works for a metals company in the northern Nile Delta and travelled to Cairo for Wednesday's demonstration in support of Shenuda.
Under Egyptian law, church building permits are strictly regulated, while those for mosques are more easily obtained.
For Cairo-based Coptic lawyer Magdi Sabry it does not matter that the court ruling followed a complaint by a divorced Copt wishing to remarry, and not by an Islamist or anyone else.
Egyptian justice "would never have dared interfere in Sharia," or Islamic law, he says. "Then why did they do this for the Coptic religion?" he asks.
Copts of a liberal persuasion admit it is hard to have their voices heard.
"These protests signal the growing religiosity among the Copts as well as the Muslims," says Kamal Sakhar, who heads an organisation for secular Copts that has several thousand members.
Allowing civil weddings without religious obligations "would reduce the pressure on the church, which could then be less defensive regarding divorce," he says.
Divorced Copts also admit they are affected by the polemic.
"It is difficult for me to make (the church) apply the judgement. I cannot oblige the church to yield with the decision of the court," says Magdi William.
Although present in government and in parliament, Copts feel threatened and marginalised by a rising fundamentalist Islam, represented by the powerful and influential Muslim Brotherhood.
They also complain of discrimination in some key positions inside the army, police, justice system or universities.
Since gunmen in Upper Egypt killed six Copts during the Orthodox Christian Christmas on January 6 the Copts feel even more fearful and targeted, even though authorities have said the killings were non-sectarian.