JOIN USAnother man was arrested during the attack in which "two men opened fire after midnight on the Qasr Shateh residence of Prince Nayef (and) the security forces retaliated, killing one of them," the spokesman told AFP.
The nature of the attack was "individual and isolated" and did not bear the hallmarks of any organisation, he said in reference to the Al-Qaeda terror network.
The men, who were only identified as members of the Zahrani family, were "under the influence of drugs" and one of them had a "small handgun".
State news agency SANA said a deadly shooting occurred in Jeddah at 1:00 am (2200 GMT), without reporting if it took place near the residence of Prince Nayef.
"A man fired his weapon in Abd el-Rahman al-Maliki Avenue in Jeddah" before he "was killed," it said citing police, adding that "no citizens or members of the security forces were affected."
Prince Nayef, in his late 70s, is second in line to the Saudi throne and was appointed second deputy prime minister in 2009.
He has been interior minister since 1970 and led the kingdom's crackdown on Al-Qaeda in response to a wave of attacks by the militant group between 2003 and 2006.
In August 2009, his son Prince Mohammed bin Nayef, the Saudi deputy interior minister, narrowly survived a suicide bomb attack claimed by Al-Qaeda in the Arabian Peninsula.