The Iranian flag still flew above the building on one of Khartoum's main roads across from the airport.
But an AFP reporter found the gate padlocked and no sign of anybody inside.
Tehran last week denied the centre and others had been shut on orders by Khartoum, despite generally close relations between the two countries.
A Sudanese official, speaking on condition of anonymity, said Thursday that the centres would close their doors by Sunday.
Sudan's foreign ministry told the centres to stop work and ordered their Iranian staff to leave the country.
Sudan said it acted in response to the centres' spreading of Shiite Islam, Iran's majority faith.
Sudan is overwhelmingly Sunni.
A Sudanese analyst told AFP the move by Khartoum might be in response to pressure from Riyadh, which further isolated the indebted and sanctions-hit Sudanese economy earlier this year by denying access to major Saudi Arabian banks.
Iranian warships have periodically made stops in Port Sudan, across the Red Sea from Iran's regional rival Saudi Arabia.
The group is also banned in many Gulf Arab countries.
Newspaper columnist Abdalla Rizig Abu Simazeh said Sudan will expect the Gulf Arab countries to reward its action against the Iranians.
But closing the cultural centres will not have much effect on broader Sudanese-Iranian ties and so "will probably minimise its impact in restoring Sudan's relations with the Arab Gulf countries and Egypt", Simazeh wrote in today's The Citizen.