Security officers early on Monday became suspicious of a man near the parking lot of Dr Suleiman Faqeeh Hospital, which is directly across from the US diplomatic mission.
When they moved in to investigate, “he blew himself up with a suicide belt inside the hospital parking”, the ministry added.
The area around the consulate has been cordoned off by security forces and the consulate’s staff members have been moved to a safe location.
There was no immediate claim of responsibility for the blast.
A US State Department spokesperson said US officials were working with Saudi officials to get more information on the explosion.