The Bangladesh Telecommunications and Regulatory Commission closed down the apps "for the time being" on orders from law enforcement and security agencies, a commission spokesman told AFP.
He did not give reasons for the decision, but local television station Channel 24 said Viber and Tango were shut down to prevent protesters from "exchanging information" across the country.
Viber and Tango have been popular among opposition protesters, including activists from the Bangladesh Nationalist Party (BNP) and its Islamist allies who have launched a crippling nationwide transport blockade to try to topple the government.
The protests have turned increasingly violent with activists firebombing hundreds of buses and trucks, and security forces retaliating with live bullets or tear gas.
At least 25 people have died in the latest violence including about a dozen burnt to death after protesters firebombed buses.
The government has deployed thousands of police, paramilitaries and an elite anti-militant force to crack down on the protesters. But the violence has continued unabated, disrupting transport services and shipments of garments, the country's biggest export.
The authorities also confined BNP leader Khaleda Zia to her office at the turn of the year after she called for her arch rival Hasina to stand down. Zia remains stuck in the compound.
Zia wants Hasina to call fresh elections after last year's controversial poll boycotted by opposition parties and marred by deadly violence.
The United States, Britain and the European Union have expressed concern over the latest unrest with the EU, the nation's biggest export destination, urging Hasina's government and the opposition to hold talks to resolve the crisis.