There were no immediate reports of deaths or injuries although dozens of trees were knocked down in the port city of Veracruz.
Karl, projected to produce a storm surge of as much as 15 feet above normal tide levels, made landfall about 10 miles (15 km) north of Veracruz on Friday before noon, the U.S. National Hurricane Center said.
Karl, which weakened from a Category 3 to Category 1 storm as it moved ashore, was blowing sustained winds of up to 90 miles per hour (150 kph).
The government ordered evacuations of low-lying areas in the important shipping port of Veracruz, which is also a popular destination for Mexican tourists.
More than 1,000 people were already in shelters, a state civil protection official told W Radio. Operations were suspended at Mexico's only nuclear power plant, which lay in Karl's path, officials said.
The southern part of Veracruz has already suffered extensive flooding this year and Veracruz's state governor, Fidel Herrera, warned of high winds and water.
Mexican authorities are experienced at evacuating people caught in the path of hurricanes and death tolls caused by hurricanes hitting Mexico are usually low.
"The worst is over. It's still windy but there's a lot of water. We are trying to remove fallen branches and leaves from trees, but there are too many. We are doing our best and the (water) level is increasing and about to reach homes," said Veracruz resident Antonio Cruz.
The storm poured rain in coastal areas and raised winds strong enough to bend small palm trees in Veracruz.
People trying to walk against the wind were unable to advance during heavy gusts. Light poles buckled and power went out in part of the city. Before the center of the storm hit the coast, fishermen scrambled to secure their small vessels.
The U.S. storm center said Karl was expected to dissipate as it breaks up against Mexico's coastal mountains.
As much as 10 inches of rain could soak coastal communities, with more falling in interior mountain towns in coffee-producing Veracruz state.
Karl is just one storm that has formed in the Atlantic this hurricane season. Hurricane Igor, a Category 2 storm, swirled with sustained winds of 105 mph (165 kph) as it churned on a course that could take it to Bermuda by Sunday.
Hurricane Julia was located far east of Igor and posed no immediate threat to land.