Internet services were cut across the country and the main roads and bridges connecting with the capital Khartoum shuttered, the information ministry said.
Dozens of demonstrators set car tyres on fire as they gathered on the streets of the capital to protest against the detentions, a correspondent from the AFP news agency said.
State television began broadcasting patriotic songs.
The Sudanese Professionals Association, an umbrella group of trade unions which were key in leading the 2019 anti-Bashir protests, was quick to denounce what it called a “military coup” and urged demonstrators “to fiercely resist” it.
The Arab League has expressed concern over the developments.
“Arab League Secretary-General Ahmed Aboul Gheit expressed deep concern over the developments in Sudan,” the pan-Arab bloc said in a statement.
The United States said it was “deeply alarmed” by the coup reports.
“The US is deeply alarmed at reports of a military take-over of the transitional government,” said US special envoy for the Horn of Africa, Jeffrey Feltman. “This would contravene the Constitutional Declaration (which outlines the transition) and the democratic aspirations of the Sudanese people.”
The developments come just two days after a Sudanese faction calling for a transfer of power to civilian rule warned of a “creeping coup” during a news conference that an unidentified mob attacked had sought to prevent.
Sudan has been undergoing a precarious transition marred by political divisions and power struggles since the April 2019 ouster of Mr al-Bashir.
Since August 2019, the country has been led by a civilian-military administration tasked with overseeing the transition to full civilian rule.
But the main civilian bloc – the Forces for Freedom and Change (FFC) – which led the anti-Bashir protests in 2019, has splintered into two opposing factions.
“The crisis at hand is engineered – and is in the shape of a creeping coup,” mainstream FFC leader Yasser Arman told Saturday’s press conference in Khartoum.
“We renew our confidence in the government, Prime Minister Abdalla Hamdok, and reforming transitional institutions – but without dictations or imposition,” Mr Arman added.