Religious freedom is guaranteed under Malaysian law
In the Malay language "Allah" is used to mean any god, and Christians say they have used the term for centuries.
Opponents of the ban say it is unconstitutional and unreasonable.
It is the latest in a series of religious rows in largely Muslim Malaysia, where minority groups claim their rights are being eroded.
A spokesman for the Herald, the newspaper of the Catholic Church in Malaysia, said a legal suit was filed after they received repeated official warnings that the newspaper could have its license revoked if it continued to use the word.
"We are of the view that we have the right to use the word 'Allah'," said editor Rev Lawrence Andrew.
The Sabah Evangelical Church of Borneo has also taken legal action after a government ministry moved to ban the import of religious children's books containing the word.
In a statement given to Reuters news agency, the church said the translation of the bible in which the word Allah appears has been used by Christians since the earliest days of the church.
There has been no official government comment but parliamentary opposition leader Lim Kit Siang said the decision to ban the word for non-Muslims on security grounds was "unlawful".
"The term 'Allah' was used to refer to God by Arabic-speaking Christians before Arabic-speaking Muslims existed," he said.
Religious issues are highly sensitive in Malaysia, which has a 60% Muslim population.Religious freedom is guaranteed in the law but minority groups have accused the Muslim Malay majority of trying to increase the role of Islam in the country.