Only the first floor office of the Metro Tabernacle Church was destroyed in the blaze that started a little after midnight Thursday, said church spokesman Kevin Ang.
The worship areas on the upper two floors were undamaged, and there were no injuries.
The church is located in a three-story building on a shopping street in Desa Melawati, a suburb of Kuala Lumpur, the main city of this Muslim-majority country.
The attack on the Protestant church comes days after the Kuala Lumpur High Court struck down a 3-year-old ban on non-Muslims using the word "Allah" in their literature.
The government has appealed against the court verdict, which allowed a Catholic publication to use the common word for God in the Malay language, and the High Court has suspended its decision from being enforced until the appeal is heard.
Muslims argue that "Allah" is exclusive to Islam, and its use by Christians would confuse Muslims and tempt them to convert to Christianity.
The court decision has resulted in a rash of angry comments and threats by Muslims on the Internet. Dozens of Muslim groups are planning a protest against the court decision on Friday after weekly prayers.
Friday's fire was the first time the controversy turned destructive.
District police chief Zakaria Pagan told the AP "we are still investigating" the fire and said he will issue a statement later.
Another church official quoted a witness as saying she saw three or four men on a motorcycle breaking the main glass front of the church and throw something inside, possibly a gasoline bomb. The account could not be independently confirmed.
About 60 percent of Malaysia's 28 million people are Malay Muslims, while the rest are ethnic Chinese and Indians, who follow Christianity, Hinduism and other religions.
The High Court ruling was on a petition by the Herald, the main publication of Malaysia's Roman Catholic Church. It uses the word Allah in its Malay-language edition, which is read by indigenous tribes in the remote states of Sabah and Sarawak.
The tribespeople are Malay-speaking, so Catholic officials say "Allah" is the only word they know for God.