(CNN) -- Hurricane Paloma, an "extremely dangerous" storm, made landfall Saturday night in southern Cuba after lashing Grand Cayman with high winds and heavy rain, forecasters said.
Paloma hit Santa Cruz del Sur, Cuba, about 6:20 p.m. ET, the National Hurricane Center reported. The storm's winds, which reached 145 mph earlier in the afternoon, dropped to about 125 mph at landfall, weakening Paloma to a Category 3 storm.
A hurricane warning was in effect for the Cuban provinces of Ciego de Avila, Camaguey, Las Tunas, Granma and Holguin.
The storm had dumped rain on Little Cayman and Cayman Brac -- the other two Cayman Islands -- whipping them with sustained winds of up to 140 mph (225 kmh) and higher gusts, the Miami, Florida-based National Hurricane Center said.
By 7 p.m. ET, though, the government of the Cayman Islands had discontinued the hurricane warning for Little Cayman and Cayman Brac.
About 100 people evacuated a shelter on one of the Cayman Islands after Hurricane Paloma's heavy winds and rain caved in part of its roof Saturday, the deputy director of Radio Cayman said.
Paulette Conolly said the residents were moved to another refuge after their shelter, on a bluff that runs along Cayman Brac, became one of the myriad buildings to be damaged by the Category 4 storm.
District Commissioner Ernie Scott said that 90 percent of the buildings on Cayman Brac were damaged and that about 500 people have taken refuge in shelters. iReport.com: Are you in Paloma's path?
Because of the damage, more people are expected to seek shelter, and the government is working on a plan to provide temporary accommodations for residents, he said.
Paloma flooded crops and downed trees on the main island of Grand Cayman, but reports of damage to buildings were few. Supermarkets and a bank had resumed business as of early Saturday afternoon, Conolly said.
"The damage here in Grand Cayman is not devastating at all. I think we are back up and running with our infrastructure and electricity and everything else," said Kurt Tibbetts, the islands' leader of government business, a ministerial post that heads the Cabinet.
Water and electricity should be restored across Grand Cayman by day's end, he said.
However, he added, "Cayman Brac and Little Cayman, they're taking a battering."
Conolly said reports came in of utility poles lying in the road, flooded thoroughfares and shipping containers from the Cayman Brac port flung into the streets.
Conolly said people in the smaller Cayman Islands also were reporting that some houses were in shambles.
"Our homes are made to withstand hurricane-force winds; they're made of steel and concrete," she said.
Tibbetts said residents are accustomed to storms, "but this one crept up a little bit fast."
Authorities were trying to clear roads on the smaller islands so they could assess the situation, Conolly said, and no one had reported storm injuries.
According to forecasters, the storm's projected path steers it across Cuba overnight and away from the U.S. mainland, into the open waters of the Atlantic.
The storm is expected to produce rainfall of 5 to 10 inches over Little Cayman, Cayman Brac and central and eastern Cuba, with 20 inches possible in some regions. Flash floods and mudslides are possible, forecasters said.
The hurricane center also warned that storm surge flooding of up to 25 feet, "accompanied by large and dangerous battering waves," was possible along the south coast of Cuba as Paloma neared landfall.
Cuban television was broadcasting messages telling viewers not to cross swollen rivers, to avoid fallen cable and to evacuate if told to do so by Civil Defense officials.
In Las Tunas, students in boarding schools were sent home, as the schools will be used as shelters.
Evacuations were under way in some coastal areas prone to flooding. Rice and cereal were being shipped to other parts of the country to prevent spoiling, and no tourists were being allowed to enter many areas..
CNN's Morgan Neill in Havana, Cuba, and Rory Suchet in Atlanta, Georgia, contributed to this report.