Officers said they held four young men who joined revellers at the main new year parade at Dhaka University seeking to hold a rally in support of gay rights, which had been denied permission.
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Authorities had cancelled the rally, being organised by activist group Roopbaan -- which says it promotes freedom of love and gender equality -- at the last minute, after some hardline Muslims threatened to beat up participants.
"We've held them after they attempted to hold a rainbow rally in support of homosexuals," local police chief Abu Baker Siddique told AFP.
"The rally did not have permission from Dhaka Metropolitan Police and the Dhaka University authorities," he said.
He said the four were expected to be released in the evening.
Gays and lesbians suffer discrimination and worse in Bangladesh where homosexuality is a crime punishable by a maximum life term, although prosecutions are rare.
However, the Roopbaan rally, which was denied permission late on Wednesday, had been allowed to go ahead in the previous two years.
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"We did not hold the rainbow rally although some 60 people came to the spot where we were scheduled to meet," a Roopbaan organiser said on condition of anonymity, adding he did not know why the four men were detained.
Police have stepped up their hunt for militants as Bangladesh reels from a series of deadly attacks on religious minorities, secularists and foreigners in recent months.
Hardline clerics have branded the Bengali new year celebrations, in which people carry masks of animals and colourful garlands, as "un-Islamic and Haram (forbidden)".
As the sun rose Thursday hundreds of girls wearing traditional red and white saris, sang and danced to mark the Bengali year of 1423 at Dhaka's colonial-era Ramna Park.
Thousands later joined the main street parade, carrying the colourful replicas of animals, hats and garlands. Security was tight with hundreds of police guarding the main venues.
Authorities also this year banned outdoor evening concerts and masks, commonly worn during the new year parades, as part of increased security.
In 2001 a new year bomb blast in Dhaka's Ramna Park killed 10 people. Eight militants were sentenced to death for the attack.
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