The NHC said Katia was likely to bring “life-threatening flash floods and mudslides, especially in areas of mountainous terrain.”
The storm comes just hours after Mexico experienced its worst earthquake in its history, measuring 8.2 magnitude.
The death toll currently stands at 15 after the killer quake struck jut before midnight, 76 miles southwest of the town of Pijijiapan.
Homes were reduced to rubble, electricity has been knocked out for more than half a million people, and schools and buildings are shut across the country.
And potentially catastrophic tsunamis are now racing towards coasts across the world – with tsunami waves expected to reach as far as Russia and New Zealand.
Waves of around 10 ft are expected to slam into Mexico’s coast, the Pacific Tsunami Warning Centre warned, with smaller waves expected across Central American countries, including Guatemala, Honduras, Mexico, El Salvador and Costa Rica.
Speaking about Katia, AccuWeather Hurricane Expert Dan Kottlowski, said: “The hurricane will bring strong and perhaps damaging winds to coastal areas within 50 to 60 miles of the landfall point.
“Rainfall totals will average 5 to 10 inches with localized 15- to 20-inch amounts.
“This will lead to life-threatening flash flooding and, for the higher terrain, mudslides.”
It is highly unusual to have three hurricanes in the Atlantic basin at the same time – the last being 2010 – and even rarer for them all to be expected to make landfall on the same day, Saturday.