An extra 250 police officers joined increased patrols at churches and mosques, including the Church of the Assumption which was attacked early Monday morning, the Malaysian Insider reported.
The Catholic church was attacked with two Molotov cocktails and a banner with the words "Allah" was found outside the building, police said.
Penang Police Chief Abdul Rahim said only one of the two Molotov cocktails exploded. No one was injured.
"Initial investigations showed that two men on a motorcycle committed the crime," he said.
The George Town attack is the latest incident involving banners bearing the word "Allah" being unfurled at churches in Penang, on the northwest coast of Peninsular Malaysia by the Strait of Malacca.
The acts were condemned last week by a senior member of the Penang branch of the United Malays National Organization, Malaysia's largest political party.
UMNO, an avowedly Islamist party, is one of a dozen or more political parties that make up the umbrella political group Barisan Nasional -- National Front -- that has been in power for most of the years since Malaysia gained independence from the British in 1957.
State news agency Bernama reported banners wrapped around perimeter walls and fencing of churches read, "Allah is great, Jesus is the son of Allah."
Penang UMNO Liaison Committee Chairman Zainal Abidin Osman said the action was an attempt by "irresponsible elements" to create religious tension in the state.
"We strongly condemn such action," he said. "We want the police to carry out a thorough investigation into the hanging of the provocative banners and take action against those responsible."
Allah is the Arabic word for God and commonly used in the Malay language to refer to God. But religious tensions often have focused on the use of the word "Allah" by groups other than Muslim organizations.
A national census in 2010 found about 61 percent of Malaysia's 29 million people are Muslims, Buddhists account for nearly 20 percent and Hindus 6 percent. Christians make up about 9 percent of the population.
The Court of Appeals overturned in October a lower court ruling that allowed the Christian Herald newspaper to use the word "Allah" to refer to God. Christian and other religious groups have said disallowing them from referring to God as Allah is against their religious freedoms.
The lower court's 2009 ruling in favor of the Herald using the word Allah increased religious tensions.
Sacks containing the severed heads of four wild boars were found at two mosques in Petaling Jaya, a city adjacent to Kuala Lumpur, in January 2010, sparking fears among government leaders and police of religious clashes.
The pig heads were the latest a series of tit-for-tat incidents at the time aimed at churches and mosques, Bernama reported.
Earlier this month, authorities in Selangor state raided the offices of the Bible Society of Malaysia and confiscated about 340 Bibles that used the word "Allah" for "God."
The seized materials comprised 310 copies of Bibles in Bahasa Malaysia, or al-Kitab, 20 copies in the Iban language, also known as Bup Kudus, and 20 copies of Luke's Gospel in Bahasa Malaysia.