The hurricane knocked down trees, signs and power poles in the fishing port of La Paz and cut power to part of the city.
"Our big job now is to take care of the people in the shelters" at local schools, said Juan Manuel Rivera, civil defense director for Baja California Sur state. He said there were no immediate reports of deaths or injuries.
One of those who abandoned a cardboard dwelling for the safety of a university campus was Abram Pineda, 22.
"We left our house last night because it felt like the house was going to blow away," he said.
For others, it merely meant an interrupted fishing vacation.
"It could have been worse. It could have caught us while we were out there," said Buddy Holt, 36, of Dallas, as he watched the choppy water off of La Paz's boardwalk.
By Monday, the hurricane's winds weakened slightly to 85 mph but it was still just 20 miles northeast of La Paz.
Forecasts indicated the storm might bring rainfall to the southwestern United States as it advances and weakens, but forecaster Dave Roberts at the National Hurricane Center said, "I wouldn't think it would be drastic."
The storm's predicted course, adjusted slightly westward on Monday, would have Ignacio march slowly up the Gulf of California over the tourist town of Loreto, then cross the peninsula and emerge near Rosarito, another popular tourist area.
Authorities closed all ports in Baja California Sur on Sunday and tried to convince residents of low-lying shanty towns to move into shelters set up in schools.
"If they won't leave, we'll ask the army to go in and get them out of their houses," said Gov. Leonel Cota. "We have to evacuate them for their own good."
State officials said Sunday night that flooding had cut one coastal highway, and a few beach huts had been destroyed, but they called the damage minor. They were concerned most about shantytowns of cardboard shacks built practically in riverbeds, like the hamlet of Agua Escondida on the outskirts of La Paz.
Communities hunkered down together. A dozen people gathered on the ground floor in Juan Lopez' food store — one of the few solid two-story buildings in Agua Escondida. A dozen more were expected, as Lopez' wife, Maria Elena Armendariz, prepared to feed them all.
"We've been here for 24 years," Armendariz said, "and we're not leaving now."
Small fishing boats were pulled out of the water and moored to palm trees around La Paz. Larger boats were either tied up to docks or headed out to sea to ride out the storm.
The hurricane bypassed the resort city of Cabo San Lucas, known for its deep sea fishing and golf courses.
Ignacio's center remained over the gulf Monday. The storm drifted slowly northwest along the eastern edge of the Baja California peninsula at about 3 mph.
Hurricane-force winds extended out up to 25 miles from the center, and tropical-storm force winds extended out up to 70 miles.
The National Hurricane Center in Miami said rainfall of more than 20 inches could cause life-threatening flash flooding and mud slides.
Martin Cruz, a 33-year-old construction worker, left his house in the hamlet of Progreso with daughters Isabel, 5, Reina, 8, and wife, Angela. They took shelter in a university.
Flo and Jim Rhodes, a couple from Scottsdale, Ariz., touring the Mexican coast, tied their yacht Inspiration to a dock as the wind picked up and rain started to fall on the La Paz marina.
"We're going to ride it out right here," said Jim Rhodes.