Willa made landfall near Isla del Bosque in Sinoa province, about 50 miles away from the major coastal city of Mazatlan.
It is currently moving north-eastwards across Mexico where it is expected to lose strength rapidly, and is likely to become a tropical storm or depression on Wednesday.
Jose Garcia, a 60 year-old resident of Escuinapa near the storm’s path, described the hurricane as “really strong”.
Speaking by phone he added: “People were very alarmed.”
Thousands were evacuated from coastal areas before the hurricane arrived.
Antonio Eehevarria, Governor of the state of Nayarit, urged those in the storm’s path not to underestimate its danger.
He said: “Let’s not play the macho. Let’s not act like superheroes
“It’s a very strong hurricane, very potent, and we don’t want any tragedies.”
However, some were either unwilling or unable to flee.
In the coastal city of Mazatlan, a major tourist hub, 182 people took refuge in the city’s main convention centre which had been turned into a shelter.
Rosa Maria Carrillo, together with her five children, was amongst those inside.
She said: “My house is made of sheet metal, wood and cardboard and I’m scared it will fall on top of me.
“Hopefully this is just a bit of water, nothing more.”
Mexico’s National Meteorological Society warned that buildings within 500 meters of the coastline were at risk of physical damage and power loss.
Hurricane Willa briefly reached category five strength on Monday, although it had been reduced to a category three storm by the time it made landfall.
According to the US based National Hurricane Centre, areas in the path of the storm could be hit by up to 18 inches of rain.
While the storm is expected to dissipate significantly, it could still bring heavy rain to Texas later in the week as it continues its journey northwards.