"This guy, he escaped from prison," the minister said. "People facilitated his escape, he is gone."
Ibrahim added that suspects who aided al-Rawi's escape "were arrested and are going to court".
But he did not detail how many conspirators had been detained, or when al-Rawi had escaped.
Earlier on Sunday, al-Rawi's re-trial at Baghdad's Central Criminal Court was adjourned until September 19, with a justice official and a lawyer for Hassan's family saying authorities had not been able to locate the defendant for more than a month.
Hassan's kidnap and murder, one of the most high-profile killings to follow the US-led invasion of 2003, sparked international revulsion and widespread sympathy among Iraqis.
"This guy, he escaped from prison. People facilitated his escape, he is gone"
Busho Ibrahim, Iraq's deputy justice minister
Born in Dublin, she had lived in Iraq for 30 years when she was taken hostage in October 2004 and shot a month later.
She was pulled from her car by men in police uniform as she was being driven to work. Her body has never been found.
The 59-year-old was head of operations in Iraq for Care International, the humanitarian group for which she worked for around 12 years. She was one of the most experienced aid workers in Iraq and had opted to stay on to continue her work after the invasion.
Hassan, who was married to an Iraqi and held British, Irish and Iraqi citizenship, was shown in several video messages pleading for her life and calling for British forces to withdraw from the country.
Her family had been counting on al-Rawi to reveal where her body had been disposed of after the appeal proceedings had been exhausted so that they could give her a proper burial.
The lawyer for the victim's family, speaking on condition of anonymity, said the court had sent a letter to the justice ministry to inquire about al-Rawi's whereabouts.
"Until now, the justice ministry has not sent a reply, so the case was delayed," the lawyer said.
Al-Rawi, from Baghdad's Jamaa district where Hassan was abducted, was jailed after having been sentenced to life in prison on June 2 last year.
He was found guilty of "participating in the killing and kidnapping of Margaret Hassan, and of attempting to blackmail her family."
Arrested in May 2008, he had pleaded not guilty to her murder, although his defence acknowledged he may have played a part in a blackmail plot.
His lawyers have claimed that an alleged confession put before the court of first instance was extracted under torture, and his retrial had originally been scheduled to begin in April, but has repeatedly been delayed.
Britain voiced concern over al-Rawi's apparent disappearance in a telephone conversation on July 23 between William Hague, the foreign secretary, and Hoshyar Zebari, his Iraqi counterpart.
In June 2006, another man, Mustafa Mohammed Salman al-Juburi, was sentenced to life in prison after being convicted of aiding and abetting the kidnappers.
His sentence was later reduced on appeal.
The hostage-takers, who called themselves "an armed Islamic group", later demanded $1m in return for Hassan's body.