Each vaccine dose costs $50, and only 500,000 doses are currently available, Dr Chikuwe Ihekuwazu, head of Nigeria's Centre for Disease Control said.
The outbreak which is said to be spreading rapidly has already killed more than 300 people.
It is the worst to hit Nigeria since 2009 when it killed 156 people.
Since December, 2,524 cases including 328 deaths have been reported from across the country.
The predominant type of meningitis causing the outbreak is type C, which is unusual.
Nigeria, which lies on the meningitis belt, stretching from the Sahel region to the Horn of Africa, is used to type A meningitis outbreaks.
"The government has mounted a significant response which will culminate in a broad vaccination campaign in the epicentre of the outbreak which is Zanfara state in north-west of Nigeria," Dr Chikuwe told the BBC's Newsday programme.
More doses 'needed'
"For this meningitis C, there is no widely available vaccine globally and the one that is available is extremely expensive."
Nigeria applied to a global stock held by the World Health Organization and 500,000 doses were released to the country.
But the scale of the outbreak means more doses are needed, with an additional stock of 800,000 expected to be shipped from the UK.
Over the weekend, the government urged Nigerians not to panic, noting that the epidemic is not unique to Nigeria.
Cases are reported in neighbouring countries such as Niger, Chad, Cameroon, Togo and Burkina Faso, the health ministry said.