Prince Mohammed, a nephew of King Abdullah and son of the powerful interior minister, Prince Nayef, was taken to hospital in the western city of Jeddah after suffering minor wounds, according to Saudi officials.
The bomber had approached the prince, who also works as his father's deputy minister, claiming to want to give himself up as a terrorist. He detonated his explosive vest while he was being searched.
Prince Mohammed has led his father's campaign against al-Qaeda terrorists in recent years, and would seem to have become a target himself as a result.
It was the first assassination attempt on a member of the royal family since the September 11 attacks on America, carried out by 19 al-Qaeda terrorists, all but two of whom were Saudi.
Those attacks brought a largely unwelcome spotlight on Prince Nayef, seen as an unshowy, tough but efficient conservative within the ruling Saudi royal family.
At first he refused to believe that Islamic terrorists were responsible. But since then, and particularly since a wave of bombings in the kingdom which began in 2003, he has aggressively pursued al-Qaeda cells operating there, as well as installing returnees from America's Guantanamo Bay internment camp in "rehabilitation programmes".
In all, the ministry says 991 militants have been arrested, 330 of whom were sentenced to jail terms in a series of trials last month.
The ministry announced the arrest of a further 44 suspects, along with the seizure of guns and bomb-making equipment, only last week.
The bomber struck on Thursday evening at one of the open sessions conducted by the royal family for well-wishers to pay their respects and raise concerns during the fasting month of Ramadan, which began last weekend.
The Saudi Press Agency, quoting the royal court, said he announced he was a wanted terrorist and wished to give himself up to Prince Mohammed in person.
He detonated his bomb as he was being searched.
King Abdullah, who is also in Jeddah, the main port of arrival for those conducting pilgrimages to Mecca, visited the prince in hospital immediately, according to the report. But the prince was discharged not long afterwards.
The two were shown meeting on television, with the prince saying the attack would "only increase our determination to eradicate militancy".
The prince's father is the king's half-brother and full brother to Prince Sultan, the defence minister and Crown Prince, and is thought to stand immediately behind him in the line of succession.
No-one else was seriously injured in the attack.
