According to the NOAA, winds have been clocked at 75 km/h.
The storm picked up strength on Sunday -- but forecasters believe it will not develop any further.
As of 5 a.m. EDT, Hector was centred about 480 km south of the southern tip of Baja California.
The storm is expected to continue westward towards the United States.
Hector became a tropical storm on Saturday. It has not triggered coastal watches or warnings, and poses no threat to land.
With files from the Associated Press