The storm caused extensive coastal flooding but police said there were no casualties.
The Mexican government had deployed troops to the area after a state of emergency was declared in much of Baja California.
The US National Hurricane Center has forecast that the hurricane would weaken to tropical storm intensity during the night into Thursday.
Jimena is the second eastern Pacific storm this season to strike Mexico.
Mexico has no major oil, coffee or mining interests in the area but the storm did force a meeting of Organization of Economic Cooperation and Development officials to discuss tax havens to relocate from Los Cabos to Mexico City.