Prince Mohammed bin Nayef was slightly injured in the bombing
Al-Qaeda has claimed responsibility for a suicide bombing by a militant who wanted to give himself up to Saudi Arabia's security chief.
An online statement by the al-Qaeda Organisation in the Arabian Peninsula said Abdullah al-Asiri had flown on the prince's plane from Yemen.
The prince was slightly injured in the assassination attempt.
Saudi Arabia has a policy of allowing wanted militants to return to the kingdom for rehabilitation.
In February it issued a list of 83 wanted militants living overseas, calling on them to return to their home country and resume normal life.
Last week's attack on the security chief, Prince Mohammed bin Nayef, was the first on a member of the Saudi royal family since al-Qaeda stepped up a campaign of bombings in 2003.
The man had said he wanted to personally tell the prince in his Jeddah interior ministry office that he would give himself up.