There was no immediate Saudi confirmation of the claim made by the group's military spokesman, who warned foreign companies and residents in Saudi Arabia 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.
A Houthi military spokesman, Yahya Sarea, said the attack was carried out with a Quds-2 type winged missile.
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," Sarea said.
Yemen has been mired in conflict since a Saudi-led coalition intervened in March 2015 to restore the Yemeni government ousted from power in the capital Sanaa by Houthi forces in late 2014.
Cross-border attacks by Houthi forces have escalated since late May when a truce prompted by the novel coronavirus pandemic expired. The Saudi-led coalition has responded with air strikes on Houthi-held territory.
The Houthi group controls most of north Yemen and most large urban areas. They say they are fighting a corrupt system.
Sarea said the strike had been carried out in response to the Saudi-led coalition's actions in Yemen.
Saudi Arabia finished hosting a G20 summit on Sunday.