It is at least the third ceasefire to be announced since violence erupted this month but none have held.
Mr Blinken said agreement had been reached between the army and the paramilitary Rapid Support Forces (RSF) after 48 hours of negotiations.
BBC reports at least 400 people have been killed since fighting erupted on 15 April.
UN Secretary General António Guterres has warned the violence in Sudan risks causing a "catastrophic conflagration" that could engulf the whole region and beyond.
The RSF backed up Mr Blinken's announcement, saying they affirmed their "commitment to a complete ceasefire during the truce period". The army did not immediately comment on the news.
Since the violence began, residents of the battle-scarred capital Khartoum have been told to stay inside, and food and water supplies have been running low.
The bombing has hit key infrastructure, like water pipes, meaning that some people have been forced to drink from the River Nile.
There will be hopes the ceasefire will allow civilians to leave the city. Foreign governments will also hope it will allow for continued evacuations out of the country.
Countries have scrambled to evacuate their diplomats and civilians as fighting raged in central, densely populated parts of the capital.
Earlier on Monday, Mr Blinken said that some convoys trying to move people out had encountered "robbery and looting".
The US, he added, was looking at potentially resuming its diplomatic presence in Sudan but he described the conditions there as "very challenging".
Sudan is suffering an "internet blackout" with connectivity at 2% of ordinary levels, monitoring group NetBlocks said on Monday. In Khartoum, the internet has been down since Sunday night.
It is estimated that tens of thousands of people, including Sudanese citizens and those from neighbouring countries, have fled because of the unrest.
Violence broke out primarily in Khartoum, between rival military factions battling for control of Africa's third largest country.
This came after days of tension as members of the RSF were redeployed around the country in a move that the army saw as a threat.
Since a 2021 coup, Sudan has been run by a council of generals, led by the two military men at the centre of this dispute - Gen Abdel Fattah al-Burhan, the head of the armed forces and in effect the country's president, and his deputy and leader of the RSF, Gen Mohamed Hamdan Dagalo, better known as Hemedti.
They have disagreed on the direction the country is going in and the proposed move towards civilian rule.
The main sticking points are plans to include the 100,000-strong RSF into the army, and who would then lead the new force.
Gen Dagalo has accused Gen Burhan's government of being "radical Islamists" and that he and the RSF were "fighting for the people of Sudan to ensure the democratic progress for which they have so long yearned".
Many find this message hard to believe, given the brutal track record of the RSF.
Gen Burhan has said he supports the idea of returning to civilian rule, but that he will only hand over power to an elected government.