The top-level category five storm is expected to be an “extremely dangerous major hurricane”, the National Hurricane Centre (NHC) said, which could produce a “life-threatening storm surge”.
Some areas may see as much as 18 inches (45cm) of rainfall, the NHC added.
While Willa is expected to weaken before making landfall, it may still pose major hazards.
It was about 135miles southwest of the town of Cabo Corrientes on Monday, and is due to reach land on Tuesday afternoon or evening.
Initially it is expected to pass over, of near, a set of islands – the Islas Marias – which are about 60 miles offshore and include a nature reserve and federal prison.
Once it reaches shore, it could strike close to the popular beach resort of Mazatlan, which has a population of about 500,000, while several other tourist destinations are in its path.
A town a few miles inland with almost 60,000 people in and around it – Esquinapa – is also projected to be hit.
Schools close to the coast in Sinaloa and Nayarit states have been ordered to close, and emergency shelters are being prepared.
Further south, Tropical Storm Vicente has weakened but is still expected to bring heavy rainfall and flooding to parts of southern and southwestern Mexico.