Nora, which has weakened to a tropical storm, has killed one boy over the weekend after torrential rains and heavy winds caused a building the popular resort town Puerto Vallarta to partially collapse.
Nora was about 165 kilometres north-west of Mazatlan on Sunday evening and moving north-northwest at 20km/h, the National Hurricane Center (NHC) said.
It was blowing at 95km/h with higher gusts.
In Puerto Vallarta, a river burst, destroying a bridge, flooding roads and bringing a building to collapse, a Reuters witness said.
Earlier, Nora was a Category 1 hurricane, the lowest rating on a five-step scale.
The body of a minor was recovered from a partially collapsed hotel, Jalisco Governor Enrique Alfaro said on Twitter. It was not immediately clear whether the second person that had also been missing, a woman, has been located.
"This tragedy was caused by the partial collapse of a hotel in downtown Puerto Vallarta, due to the overflow of the Cuale River," Alfaro wrote.
"To his family, who came to our port from Spain 7 years ago, and to his loved ones, all our support and our deepest condolences. R.I.P."
Elsewhere, local media showed pictures of flooding, felled trees, damaged roads and power lines across several states.
The Miami-based NHC expected Nora to continue moving north-northwest on Sunday in its latest advisory and then move slower northwest through Tuesday.
"Gradual weakening is forecast during the couple of days as the centre moves roughly parallel to the coast of Mexico," the NHC said.
"However, rapid weakening will likely occur if the centre moves inland sooner than forecast."
Nora will likely produce additional heavy rainfall along the west coast of Mexico from the states of Jalisco to Sonora through late week, the NHC said.
It could also produce life-threatening flash flooding and mud slides, as well as storm surge and large waves.
Last week, Hurricane Grace killed eight people after it hit Veracruz.
Australian Associated Press