Alam, 63, who accused police of assaulting him in custody and was earlier sent to a hospital for a check-up following an order from the high court, was taken to a magistrate's court late on Sunday.
“The court then sent him to jail,” police official Moshiur Rahman told AFP.
Another police officer told the local Daily Star newspaper that Alam would be kept in prison until the completion of the probe into his charges.
Alam was accused of making “false” and “provocative” statements on Al Jazeera and on Facebook Live as tens of thousands of students protested in Dhaka in late July and early August.
He also published photos of the demonstrations.
He is being investigated for allegedly violating Bangladesh's internet laws, enacted in 2006 and sharpened in 2013, that critics say are used to snuff out dissent and harass journalists.
Alam, whose work has appeared widely in Western media and who founded the renowned Pathshala South Asian Media Institute, faces together with others a maximum 14 years in jail.
New York-based Human Rights Watch and London's Amnesty International have demanded his release.
The renowned photographer told reporters outside court last Monday that he had been beaten so badly in police custody that his tunic needed washing to get the blood out.
Alam's arrest capped a turbulent week in Bangladesh as students poured onto the streets in Dhaka and elsewhere for nine straight days after two teenagers were killed by a speeding bus.
Last weekend the demonstrations turned violent as some protestors vandalised and torched vehicles and police used tear gas and rubber bullets. Mobs allegedly aligned with the government and wielding metal rods attacked demonstrators, journalists and even the US ambassador's car. Some 150 people were injured.
Although the protests fizzled out last week, Bangladesh authorities launched a crackdown on online activists for “spreading rumours” to fuel the unrest.
Police are looking for people behind some 1,000 Facebook accounts and have arrested at least a dozen social media activists. These include a television actress and the head of an online media outlet.