Located about 565 kilometers (350 miles) south of the tip of the peninsula, the storm was traveling north-northwestward at 23 kilometers per hour, the Miami-based US National Hurricane Center said.
Octave had top winds of 80 kilometers per hour that could begin to weaken gradually starting Monday, it added. There were no hazards affecting land.
Mexico's National Weather Service said Octave would trigger rains in the northwestern part of the country, noting that heavy downpours could cause flooding in urban areas.
Rivers may also overflow and trigger landslides in mountainous regions, the weather service added.
Octave was approaching just three weeks after hurricanes Manuel and Ingrid whipped the country simultaneously from coast to coast, causing severe damage in several states.
At least 157 people were killed in the historic downpours, including 101 in Guerrero state alone. Dozens were left missing in the mountainous village of La Pintada after a landslide buried a third of the community.
September's torrential rains left 1.7 million people homeless.