Al-Shanqiti is close to the Jordanian sheikh Abu Muhammad al-Maqdisi, the mentor of Al-Qaeda's leader in Iraq, Abu Musab al-Zarqawi, who was killed in a US raid there in 2006.
"How should Sharia (Islamic) law view Coptic priests and Christians who proselytise in our country and kidnap our women?" said al-Shanquiti's message, cited by jihadist website Al-Tawed.
"You should attack those who attack you, with a force that is equal to or greater than theirs."
"The Koran endorses the principle of 'an eye for an eye', a tooth for a tooth."
He claimed jihadist leaders had decided to avenge the alleged kidnapping of the Muslim women, named in unconfirmed reports as Wafa Costantine and Camelia Shehata.
"These Christians who don't hand over Muslims and who have kidnapped those two women have violated the accord under which they are afforded protection. We have no obligations towards them," said al-Shanquit.
He recalled that the Al-Qaeda linked group which claimed the deadly attack on 31 October against a Christian church had in its message called for the release "of prisoners held by the Christian church."
The attack on the Baghdad church killed 58 people including two priests and injured 80 others and drew international condemnation.
Al-Shanqiti is a member of Al-Tawed's sharia committee and his 'fatwa' was was an apparent response to a question from a user of the website nicknamed 'Abu Isa the Egyptian'.
In a phone call on Monday, Italy's prime minister Silvio Berlusconi expressed condolences to Egypt's president Hosni Mubarak over the suicide bombing of the Coptic church in Alexandria on 31 December. At least 21 people died and dozens were injured in the attack, which has sparked violent protests in the country by Coptic Christians.
Pope Benedict XVI on Sunday deplored the attack in an address as "vile gesture" and US president Barack Obama called it a "heinous act".
Italy's Il Foglio newspaper reported on Monday that Orthodox Coptic Christians plan to hold a demonstration in the Italian capital, Rome, on Sunday to protest the attack against the church in Alexandria and to demand that the Egyptian government do more to protect Copts.