The internet was almost entirely shut down from 18:30 GMT (01:00 local time).
In the northern state of Kachin, the security forces fired shots at a protest – the ninth day of anti-coup demonstrations across the country.
A UN official accused the military of “declaring war” on the people.
Tom Andrews, the UN special rapporteur on Myanmar (also known as Burma), said the generals were showing “signs of desperation” and would be held accountable.
Western embassies urged the military to show restraint.
A statement signed by the EU, the US and the UK said: “We call on security forces to refrain from violence against demonstrators, who are protesting the overthrow of their legitimate government.”
The coup in Myanmar removed the civilian government led by Aung San Suu Kyi. Her party won a resounding victory at the election in November, but the military said the vote was fraudulent.
Ms Suu Kyi is now under house arrest. Hundreds of activists and opposition leaders have also been detained.
Across the country, hundreds of thousands of protesters rallied against the military for the ninth day in a row.
In the city of Myitkyina, in Kachin state, shooting could be heard as security forces clashed with anti-coup demonstrators. It was not clear whether rubber bullets or live rounds were being fired.
Five journalists were among those arrested.
In Yangon, armoured vehicles were seen on the streets for the first time since the coup. Monks and engineers led a rally there, while motorcyclists drove through the streets of the capital, Nay Pyi Taw.
Telecoms operators in Myanmar said they had been told to shut off internet services from 01:00 to 09:00 local time, Sunday into Monday (18:30 to 02:30 GMT).
Internet traffic was at 14% of normal levels after the order came into force, according to NetBlock, a monitoring group.
A doctor at a hospital in Nay Pyi Taw told the BBC the security forces were carrying out night-time raids on homes.
“I’m still worrying because they make a curfew statement just not to go outside between 20:00 and 04:00, but this makes a time for the police and soldiers to arrest people like us,” said the doctor, who cannot be named for safety reasons.
“The previous day they stole into the house, cut down the fence, entered and arrested people unlawfully. That’s why I’m also worrying, yeah.”
An office of the US embassy in Yangon warned US nationals to stay indoors during curfew hours.
On Saturday, the military said arrest warrants had been issued for seven prominent opposition campaigners and warned the public not to harbour opposition activists fleeing arrest.
Video footage showed people reacting with defiance, banging pots and pans to warn their neighbours of night-time raids by the security forces.
The military on Saturday also suspended laws requiring court orders for detaining people longer than 24 hours and for searching private property. (Courtesy BBC)