The US National Hurricane Centre said Norma, once a Category 4 hurricane, made landfall as a Category 1 hurricane with winds of 128km/h just south of Todos Santos.
Norma is expected to continue weakening over the weekend as it crosses into the Sea of Cortez, also known as the Gulf of California.
Norma is expected to bring heavy rain and potential flash floods to the Baja area and may hit the mainland coastal state of Sinaloa as a tropical storm.
Earlier, residents of the Los Cabos resorts rushed to prepare as Norma approached.
Businesses in Cabo San Lucas nailed up sheets of plywood over their windows, and government personnel hung up banners warning people not to try to cross gullies and stream beds after Norma regained strength and once again became a major storm on Friday.
According to the national civil protection agency, shelters in Baja California housed some 1500 people by Saturday morning.
The Los Cabos civil defence agency urged residents to stay indoors all day as winds and rain increased. Emergency workers rushed around the city evacuating people from low-lying areas and moving them to shelters.
Police in San Jose del Cabo rescued two people from their truck when a surging stream swept it away early Saturday.
Hotels in Los Cabos, which are largely frequented by foreign tourists, remained about three quarters full and there was no major move by visitors to leave, tourism official Maribel Collins said.
With rain already falling in Los Cabos, some flights in and out were cancelled on Friday, there was no way out anyway. Airports were closed on Saturday, according to the local civil defence office.
The local hotel association estimated there were about 40,000 tourists still in Cabo San Lucas and San Jose del Cabo on Friday.
Homero Blanco, the state commander of the National Guard, said beaches at the resort had been ordered closed and guard troops were sent to clear people from the shore.
The federal government posted 500 marines to the resort to help with storm preparations, and municipal officials said as many as 39 emergency shelters could be opened if needed.