Demonstrations were held outside two mosques in Kuala Lumpur, The New York Times reported.
"Allah is only for us," said Faedzah Fuad, 28, who brought hand-made signs with her. "The Christians can use any word, we don't care, but please don't use the word Allah."
Allah, which means God in Arabic is commonly used in many Arabic-speaking countries and in Indonesia to refer to the Christan and Jewish God. A court ruled Wednesday that a Catholic newspaper could use the word in its Malay edition.
The government is appealing the ruling, but Prime Minister Najib Tun Razak condemned the arson attacks and denied the government condones the violence.
Najib ordered police to strengthen security at all places of worship, Malaysia's Bernama news agency reported.
"I condemn such action by the irresponsible people because it can harm the cordial relationship and harmony that has been in existence," the prime minister told reporters. "As a multiracial community we must practice respect for one another."
Notable deaths of 2014 [PHOTOS]
Syrian Al Qaida group executes Lebanese soldier