Fire in Friday's first incident gutted the administrative office on the first floor of the three-storey Metro Tabernacle church, shortly after midnight.
Mohamad Sabtu Osman, the Kuala Lumpur police chief, said a witness saw four people on two motorcycles breaking the glass front of the church and throwing an incendiary object inside before fleeing.
Molotov cocktails were believed to be thrown into the compounds of two other churches in Petaling Jaya, just outside the capital, before dawn on Friday.
The attacks on the Assumption church and the Life Chapel caused minor damage, officials said.
Osman said there were no fatalities in the attacks and police were investigating, but added that it was premature to link the attacks on the churches to protests by Muslim groups over last week's court ruling.
Lawrence Andrew, the editor of the Herald, said many churches had employed extra security guards amid protest threats as a precaution for fear that matters "may just blow up".
And police say they have stepped up security at churches nationwide following the attacks.
Musa Hassan, the nation's police chief, said he had "instructed all patrol cars to patrol all church areas - we are monitoring all churches".
Najib Abdul Razak, Malaysia's prime minister, condemned the attacks "because they will destroy our country's harmony".
"The government will take whatever steps it can to prevent such acts," he said.
Salahuddin Ayub, a leader from the Islamic opposition party PAS, also condemned the attack, saying Islam does not allow followers to destroy houses of worship belonging to non-Muslims.
|A court ruling last week that the Herald may use the word 'Allah' has been suspended [EPA]
"Even during war, those who seek sanctuary in houses of worship cannot be killed or the buildings itself destroyed," he was quoted as saying by the Malaysian Insider website.
Azmi Sharom, a columnist and law professor at Universiti Malaya, told Al Jazeera that "the unrest is not surprising because of the fact that the government has been pandering to these kinds of people for a long time".
He said the government allowed some groups to protest when others were banned because the main ruling Umno party - which depends on the Malay/Muslim demographic to remain in power - was "unwilling to do anything which would seem to go against what they think is the Malay/Muslim desire".
"This is a noisy demographic and it is potentially dangerous for Umno to alienate them, so this will be a real test for Najib's administration," he said.
Malaysian Muslims, he added, must stand up – "now or never" - against such behaviour as the attacks and say "no, this is not a part of what we are".
Muslim groups plan to hold protests after prayers on Friday against the court overturning the "Allah" ban, despite police chief Musa's advise to organisers to "let this be handled by the court" and warning that he "will take action against anyone who acts to jeopardise national security".
The prime minister earlier said his government was powerless to stop the planned protests as long as protesters did not leave their mosques.
"We cannot stop the people if they want to congregate within the mosques' compounds," he said.
"Hopefully it does not spill over to something more serious," he said, adding that "this matter should be resolved through the courts in an amicable way".
"If they become unruly, the police will know what to do."
Muslims in Malaysia argue that the "Allah" is exclusive to Islam, and its use by Christians would confuse Muslims.
But Catholic church officials say that for Christian indigenous tribes in East Malaysia, who are the main readers of the Herald's Malay-language edition, "Allah" is the only word they have known for God for decades.