According to the US National Hurricane Centre, the Hurricane, which formed in the eastern Pacific Ocean near Mexico on Sunday, Jun 20, is moving away from the land.
With winds up to 80 mph (130 kph), Hurricane Celia was 370 miles (600 km) south of the tourist resort of Acapulco and was moving toward the west, away from Mexico, at 7 mph (11 kph), the centre said.
"Celia is a Category One hurricane on the Saffie-Simpson scale. Some strengthening is forecast during the next 48 hours," the centre said in a Public Advisory posted on its website.
Celia has turned away from Mexico's lifeline - the oil export facilities, which are in the Gulf of Mexico.
Blas, the second storm of the hurricane season has also weakened and has downgraded from a tropical storm to a tropical depression.
Weather agencies are watching the hurricanes closely as it has been predicted that the 2010 Atlantic storm season could be the most intense since 2005.
In 2005, Hurricane Katrina claimed over 1,000 lives besides crippling oil production when it hit the Gulf of Mexico facilities.