The men are being held in police custody and are likely to appear in court on Wednesday, police said.
Jamaat-e-Islami said about 25 other party members were detained overnight in various districts.
The three were accused of making comments comparing the party's chief to the prophet Muhammad.
The three leaders had been summoned to appear at a Dhaka court on Tuesday but ignored the order, which lead to an arrest warrant being issued, Haque said.
He said the charges stemmed from claims that Nizami's alleged persecution at the hands of the ruling Awami League was akin to the suffering of the Prophet Mohammed, he said.
Jamaat-e-Islami supporters have condemned the arrests as politically motivated because of the group's political alliance with the opposition Nationalist party, led by Begum Khaleda Zia, the former Bangladeshi prime minister.
Many Bangladeshis accuse Jamaat of collaborating with the Pakistani army during Bangladesh's independence war in 1971.
The party in turn has accused the administration of Sheikh Hasina of trying to curb its activities using war crime charges and is likely to see the arrests as part of that effort.
Police in Dhaka on Wednesday also clashed with hundreds of textile and garment workers who were protesting against low wages and calling for an immediate pay rise.
In the second such clash over pay in the last two weeks, workers erected street barricades and pelted police with stones. Police responded with clubs, tear gas and water cannons.
Ten policemen were among the 30 wounded in the clash.
Just three days earlier, Bangladesh was crippled by a one-day general strike.
Workers at garment factories in Bangladesh earn as little as $24 a month, manufacturing clothing for international brands like Marks & Spencer, JCPenney, Wal-Mart and H&M.