In San Pedro Garza Garcia, Mexico's richest suburb, floods from the hurricane washed furniture out of mansions and buffalo were washed out of the city zoo.
One woman was crushed to death by a mud-slide as huge rocks from surrounding mountains crashed down onto roads.
"I thought we were going to die," Lesly Ramos, a housewife, told local radio as she surveyed the mud and rocks that had filled her middle class suburban home.
Monterrey has usually been spared from hurricanes coming off the Gulf of Mexico and the city was unprepared for the storm.
The category 2 hurricane came on shore on Wednesday night, after it left 12 people dead in Central America.
The storm missed oil rigs in the Gulf of Mexico, but on Friday, surging rivers forced the closure of Femsa, a giant soft-drink manufacturer and Cemex, a global cement maker.
Kansas City Southern, a railroad company which owns tracks and runs trains in Mexico, has said that the storm had damaged some of its lines, forcing a partial shut down in cargo transport in northern Mexico.
Hurricane Alex brought 80 centimetres of rain to some districts of Monterrey.
"That is more than the accumulated amount of rain in the 365 days of the year," said Jorge Camacho, director of rescue services in Nuevo Leon state, of which Monterrey is the capital.