The attack was carried out with a Quds-2 type winged missile, Saree said in a tweet late on Sunday.
He also posted a satellite image with the label “north Jeddah bulk plant-Saudi Aramco”. Google Maps shows a facility matching that image and description on the northern outskirts of Jeddah.
“The strike was very accurate, and ambulances and fire engines rushed to the target,” Saree said.
He further warned foreign companies and residents in Saudi to exercise caution as “operations will continue”.
Aramco’s oil production and export facilities are mostly in Saudi’s Eastern Province, more than 1,000 km across the country from Jeddah.
State oil giant Aramco did not immediately respond to a request for comment.
The military spokesman said the strike had been carried out in response to the Saudi-led coalition’s ongoing airstrikes against Yemen.
The Saudi-led coalition invaded Yemen in 2015. Since then, over 100,000 people have been killed, according to the US-based Armed Conflict Location and Event Data Project (ACLED).