Two security officers were slightly wounded, the interior ministry said, as the American embassy in Riyadh reported no injuries among US consulate staff.
General Mansour al-Turki, the interior ministry spokesman, told Saudi-owned Al-Arabiya television that the bomber was not Saudi but a "resident foreigner".
Millions of foreigners, many from Muslim-majority nations in the Middle East and Asia, work in the kingdom.
The ministry did not specify if the bomber had intended to target the consulate, but an investigation was now under way.
It happened before the end this week of the holy month of Ramadan, when Muslims fast from dawn until dusk.
The interior ministry said security personnel became suspicious of the man near the parking lot of a hospital which is across from the US diplomatic mission.
When they moved in to investigate at around 2:15 am (2315 GMT Sunday) the man "blew himself up with a suicide belt inside the hospital parking lot", the ministry said.
In a security notice on its website, the American embassy noted media reports of "a suspected suicide attack near the US consulate in Jeddah" early on the morning of July 4.
"The US embassy and consulate remain in contact with the Saudi authorities as they investigate the incident," it added, urging Americans to "take extra precautions when travelling throughout the country".
In March last year the US embassy closed its main office, as well as consulates in Jeddah and Dhahran, for a few days over unspecified "security concerns".
It was not immediately clear who was behind today's incident, but since late 2014 Saudi security officers and minority Shiites have been hit by deadly violence claimed by IS.
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