Salah Gosh until last month helped Sudan's feared National Intelligence and Security Services (NISS).
Protesters say dissenters were regularly taken by the NISS to "ghost houses" where they were tortured.
The NISS has also been accused of responding to the country's ongoing protests with live bullets, tear gas and violent beatings.
Although Gosh stepped down as security chief shortly after former President Omar al-Bashir was deposed by the military in early April, demonstrators' calls for his arrest have been ignored until now.
Protesters have also decried a perceived lack of transparency in the arrest of major regime figures including Bashir.
Bodyguards stationed outside Gosh's home on Monday prevented his arrest over a bank account, the public prosecution service said.
Gosh was to be arrested for questioning over a bank account only accessible by him containing 46 billion Sudanese pounds ($1.2 billion), Reuters reported.
"Following the opening of a criminal case before the public prosecutor's office, a police force… under the direct supervision of the prosecutor and deputy prosecutor was dispatched with a warrant to arrest Gosh and search his home issued by the prosecution service," the secretariat of the public prosecution service club said in a statement on Tuesday.
"The security guards charged by the NISS with protecting the house of the accused refused to execute the warrant."
According to the statement published by leading protest organising body, the Sudanese Professionals Association (SPA), the security force stationed at Gosh's residence drove a vehicle armed with a machine gun towards the car carrying members of the prosecution service.
The security guards then refused to implement the arrest and search warrants, and threatened to shoot at the prosecutors.
"This behaviour shows the blatant violation of the law by the NISS and the control it wields over the state. It is inconceivable that this could happen in a state and under institutions governed by the rule of law," the prosecutors said.
The incident appears to indicate what many protesters have feared - impunity for figures who are accused of violating human rights under Bashir's rule.
But it also points to a crucial split between the judiciary and the security services.
The prosecutors called for the current NISS head, Abu Bakr Damblab, to resign, in addition to the restructure of the intelligence and security services and the reform of Sudan's national security law.
Sudan's ruling military council has already promised to restructure the NISS as part of negotiations with an umbrella body representing protesters.
Many activists, however, have demanded the trial of Gosh and the abolition of the security services entirely, fearing a restructure by the military would provide the same result under a different name.
The prosecutors also called for the preservation of the independence of the judiciary in the wake of the failed arrest.
The public prosecution service club has put its participation in a nationwide general strike called for by the SPA on Tuesday "under consideration", said the statement.
Gosh's Emirati and Saudi backers
Before Bashir's ouster, Gosh was reportedly tipped as the favoured successor of the UAE, Saudi Arabia and Egypt.
The former NISS chief had served as head of the security forces from 2004 to 2009, after which he was appointed as national security adviser by Bashir.
Gosh was fired in 2011 and later arrested on suspicion of plotting a coup against Bashir.
But just two years later he managed to earn a presidential pardon.
He was re-appointed NISS chief in February last year - allegedly after Saudi Arabia offered financial support to Bashir's regime.
Saudi Arabia and the UAE were among the first countries to give their backing to Sudan's military after Bashir's ouster, and both states have since gifted the country's central bank with hundreds of millions of dollars in aid.