Juliette was about 15 miles west-northwest of Cabo San Lucas, Mexico, and traveling northwest at 24 miles per hour, the National Hurricane Center in Miami said in its 8 p.m. PDT advisory.
Maximum sustained winds were 45 miles per hour with stronger gusts.
The Mexican government issued a tropical storm warning for the southern portion of Baja California from San Evaristo on the east coast to near Bahia Magdalena on the west coast, including Cabo San Lucas.
Juliette was expected to move northwesterly with a reduction in forward speed over the next 24 hours, then turn to the west-northwest with a further decrease in forward speed Thursday night.
The center of the storm was moving near or over the southern tip of Baja California Wednesday night.
Tropical-storm-force winds extended outward up to 45 miles, mainly to the east of the center.
The storm could bring rainfall of 1 to 3 inches to the southern peninsula.