Paul, which powered up from 90 mph just 3 hours earlier, was centered about 360 miles off the southern tip of Baja California and was heading to the north-northeast at 14 mph, the National Hurricane Center in Miami said in its 8 p.m. EDT advisory.
Hurricane-force winds extended up to 25 miles from Paul's eye and tropical storm-force gales reached out up to 90 miles.
The Mexican government issued a hurricane warning covering the Baja California coast from Santa Fe northward to Puerto San Andresito.
A tropical storm warning was in place from north of Puerto San Andresito to Punto Abreojos, and from Agua Blanca to south of Santa Fe, the government said.
A tropical storm watch was in effect for the Baja Peninsula from north of Punta Abreojos to El Pocito.
The hurricane center urged people in the hurricane warning area to quickly complete their preparations to protect themselves and their property.
Paul was forecast to keep on its current path into early Tuesday, then weaken as it turns to the north and slows down before veering to the north-northwest Wednesday.
The eye of the storm was projected to approach the west coast of the southern Baja Peninsula late Tuesday and be near or over the central peninsula Wednesday.
An automated station on Clarion Island clocked sustained winds at 53 mph with gusts to 77 mph.
Paul was expected to produce 2-4 inches of rain over the southern Baja Peninsula, with up to 8 inches possible.
Dangerous swells generated by Paul were expected to affect the south and west coasts of Baja California Monday night.