Outside Dhaka, protesters also targeted the newspaper’s office in the city of Rajshahi, and marched through the streets of the port city of Chittagong.
It follows protests earlier this month that targeted Dhaka’s English-language Daily Star.
Protester Alif Bin Labib Shuvo, 20, a student injured during anti-Hasina protests in July, alleged that both Prothom Alo and the Daily Star seek to “destabilise” Bangladesh.
“If they don’t change their current strategy, they should be closed,” said Mir Farhad, 35, another protester.
Interim leader Muhammad Yunus has repeatedly insisted he wants media freedom.
Press watchdogs say dozens of journalists – seen by critics as having supported Hasina when she was in power – face police investigations in apparent retaliation for their past work.
At least four are in custody, accused of inciting the killing of protesters in the days before Hasina’s downfall.
Reporters Without Borders say as many as 140 journalists are facing police investigations into violence, calling it “systematic judicial harassment”.
The US-based Committee to Protect Journalists this month urged reforms to guarantee press freedom at “this critical juncture in the country’s history”.
