There was no immediate comment from the military.
Sudan has been on edge since a failed coup plot last month unleashed bitter recriminations between military and civilian groups meant to be sharing power following the 2019 ouster of former leader Omar al-Bashir.
Bashir was toppled and jailed after months of street protests. A political transition agreed after his ouster has seen Sudan emerge from its isolation under three decades of rule by Bashir and was meant to lead to elections by the end of 2023.
The military had stirred unrest in eastern Sudan and used the crisis to implement a coup against the government of Hamdok, the director of his office told al-Arabiya TV channel.
The coup happened in spite of an agreement Hamdok had reached with the head of a ruling council, Abdel Fattah al-Burhan, in the presence of U.S. special envoy Jeffrey Feltman, he added, according to the Dubai-based channel.
The information ministry said military forces had also arrested civilian members of the Sovereign Council and members of the government.
A Reuters witness saw joint forces from the military and from the powerful, paramilitary Rapid Support Forces stationed in the streets in Khartoum.
The military was meant to pass leadership of the joint Sovereign Council to a civilian figure in the coming months.
But the timing of the handover had been left unclear, as transitional authorities struggled to move forward on key issues including whether to hand Bashir over to the International Criminal Court.
In recent weeks, civilian officials had claimed credit for some tentative signs of economic stabilisation after a sharp devaluation of the currency and the lifting of fuel subsidies.
Feltman, who was visiting Sudan on Saturday and Sunday, said the United States was deeply alarmed at reports of a military takeover of the transitional government in Sudan.
On the official Twitter of the State Department's Bureau of African Affairs, Feltman warned that a military takeover would contravene Sudan's Constitutional Declaration and puts at risk U.S. assistance.
Military forces stormed Sudanese Radio and Television headquarters in Omdurman, the twin city of the capital Khartoum, and arrested employees, the information ministry said on its Facebook page.
Two major political parties, the Umma and the Sudanese Congress, condemned what they said was a coup and the campaign of arrests.
The Reuters witness said military and paramilitary forces deployed across the capital, Khartoum, restricting civilians' movements, as protesters carrying the national flag burnt tires in different parts of the city.
Khartoum airport was shut and international flights were suspended, according to Dubai-based al-Arabiya TV channel.
Hamdok is an economist and former senior U.N. official who was appointed as a technocratic prime minister in 2019 and is well respected internationally.
Though popular with pro-democracy civilian groups, he has struggled to keep the transition going due to political splits between the military and civilians and the pressures of an economic crisis.
Family sources told Reuters that military forces had stormed the house of Hamdok's media adviser and arrested him.
Many of the ministers and officials who had been arrested had been intensifying their rhetoric towards the military in the past few weeks.
Reuters witnesses said internet services appeared to be down in Khartoum.
The Sudanese Professionals Association, a main activist coalition in the uprising against Bashir, called on supporters to mobilise after what it called the arrest of cabinet members.
"We urge the masses to go out on the streets and occupy them, close all roads with barricades, stage a general labour strike, and not to cooperate with the putschists and use civil disobedience to confront them," the group said in a statement on Facebook.
As tensions built this month, a coalition of rebel groups and political parties aligned themselves with the military and called on it to dissolve the civilian government, staging a sit-in outside the presidential palace.
Last week, several cabinet ministers took part in big protests in several parts of Khartoum and other cities against the prospect of military rule.
The military head of the Sovereign Council has previously asserted his commitment to the transition.
Aside from the political tension, Sudan is in the midst of a deep economic crisis, marked by record high inflation and shortages of basic goods, that was beginning to show signs of easing amid flows of international aid.
(Reporting by Khalid Abdelaziz, Mahmoud Mourad and Alaa Swilam; Writing by Aidan Lewis; Editing by Christopher Cushing, Robert Birsel) ((Alaa.Swilam@thomsonreuters.com;))