Bishop Oliver Dashe Dome of Maiduguri said that Western military intervention was the only viable option in the fight against the militants, now allied to Islamic State.
Boko Haram has taken over parts of Nigeria as it attempts to set up an Islamic state.
It has killed thousands of people including 2,000 in one attack last week.
In an interview with Aid to the Church in Need, the bishop said Nigeria's military was weakened by incompetence, corruption and Boko Haram infiltration within its ranks.
He warned that drastic action was urgently needed as the attacks earlier this month in strategically significant Baga showed that Boko Haram was poised to become a threat well beyond Nigeria's borders and was recruiting from Niger, Chad, Cameroon and Libya.
He said: "The West should bring in security - land forces to contain and beat back Boko Haram.
"A concerted military campaign is needed by the West to crush Boko Haram."
He added: "Among the soldiers, there were sympathisers with Boko Haram - some of them were even Boko Haram members and many of them just ran away."
The bishop described how within five years the Boko Haram threat has decimated his diocese with more than 50 churches and chapels destroyed and more than 200 churches abandoned.
He said that 1,000 of his faithful have been killed, many of them by Islamists.
"The [extremists] point a gun or a knife at them saying that if they do not convert they will be killed. Some of them have been killed for refusing to convert," he said.
Since 2009 nearly 70,000 of the 125,000 Catholics in Maiduguri have fled their homes in the face of Islamist extremism.
Bishop Oliver Dashe Dome added: "The threat we face presents a very bleak future for the Church. Many of our members are scattered and others have been killed. In some areas there are no Christians any more.
"But the Church belongs to Christ. The Church will remain strong and many of our people have returned after land has been taken back by the Nigerian soldiers.
"The most important thing is to pray for our people; I know people are praying for us and I am very grateful.
"I want people to pray the Hail Mary - our mother Mary has been championing our cause. We have a lot of devotion to the Blessed Virgin."