In the northern area of Kishoreganj, a temple was set ablaze and badly damaged Saturday. A leaflet left behind called for an end to "idol worship" and for a mosque to be built in the temple's place, the Sangbad newspaper reported.
One day later, a group destroyed statues of deities, made ahead of the major Hindu festival of Durga Puja on Thursday, in Narayanganj near the capital Dhaka.
A private guard identified as Shah Alam was arrested for the attack Sunday, police officer Ashadul Islam told AFP by telephone.
Separately, two teenagers were arrested for destroying idols in the western Natore district, Sangbad reported.
Opposition leaders have alleged persecution of Bangladeshi Hindus since Prime Minister Khaleda Zia's Islamist-allied coalition swept in to power last October.
The government has denied any campaign against Hindus, who form about 12 percent of Bangladesh's 130 million-strong population, and has assured full security for the festival Thursday.
The US State Department's 2002 International Religious Freedom Report said Bangladeshis "generally are free to practice the religion of their choice," but said police are often slow to assist minorities who are victims of crimes.
In the Narayanganj incident, local lawmaker Giasuddin Ahmed, who is from Zia's Bangladesh Nationalist Party, offered 40,000 taka (689 dollars) for the destroyed deities to be rebuilt.