The eye of the rare Category Five storm made landfall on Barbuda -- part of the twin island nation of Antigua and Barbuda -- just before 0600 GMT with winds gusting at up to 185 mph, the Miami-based US National Hurricane Center said.
The storm is headed northwest toward the Virgin Islands and Puerto Rico, with potential for storm surges of up to 20 feet (six meters) above normal tide levels, it added.
The NHC said on Tuesday that while Irma was in the Atlantic headed for the Caribbean it was the strongest hurricane ever recorded in that ocean.
Ahead of the storm, which comes on the heels of the devastating Hurricane Harvey late last month in Texas, people packed shelters, stocked up on provisions and evacuated tourist areas as far north as Florida. The storm is expected to last for days.
The NHC said in a bulletin at 0600 GMT that the eye of Irma was passing over Barbuda.
As people hunkered down in the north of the Caribbean arc known as the Leeward Islands, the NHC said Irma was a potentially catastrophic storm.
"I am just praying to God. Everything happens for a reason," an Antigua woman who gave her name as Kazia said as she endured what she called 60-80 mph winds in a town called Sea View Farm. This was hours before the eye passed over.
Davina, a woman in the town of Yorks on the same island, said: "I can hear very strong winds and things being thrown around, but I am scared to look outside."
Power was turned off across Antigua as a safety precaution because power lines are above ground. Families packed shelters. One after another, scared people sitting in the dark called in to radio stations.
The core of the hurricane was expected to move over other parts of the northern Leeward Islands early Wednesday, the NHC said.
It will then head northwest toward the Virgin Islands and Puerto Rico later Wednesday or Wednesday night.
Category Five is the highest on the scale for hurricanes in the Atlantic and Caribbean.
'I am scared'
Schools and government offices in French overseas territory Guadeloupe have been ordered shut, while hospitals are stocking up on medicines, food and drinking water. People living on shorelines will be moved to safety, authorities said.
In Guadeloupe, families filed into shelters with their children, along with tourists.
"We came here to protect our little two-year-old boy," said a tourist who only gave his first name as Ludovic.
"We hadn't prepared for this disaster scenario. Our rental home is beautiful but it only has bay windows."
Florida expects the greatest danger from Friday night through Monday.
President Donald Trump declared states of emergency in Florida, Puerto Rico and the US Virgin Islands, authorizing federal funding to help local authorities respond.
Threat to Puerto Rico, Florida
Florida Governor Rick Scott said Irma posed "a severe threat to the entire state" barely a week after Harvey claimed at least 42 lives.
Tourists in the popular Key West islands were packing their bags on a mandatory evacuation order and were due to begin leaving at sunrise on Wednesday, with a similar order for residents due to follow.
"We're emphatically telling people you must evacuate, you cannot afford to stay on an island with a Category 5 hurricane coming at you," said Monroe County emergency operations center director Martin Senterfitt.
There were long queues as people rushed to get batteries, bottled water, groceries and fuel, while many cut trees around their homes and sought to tie down objects and seal up their windows.
In a crowded supermarket in Miami Beach where people were scrambling to buy provisions, it was already difficult to find some basic supplies, like water.
"It's because people go crazy and buy up everything," 81-year-old resident Gladys Bosque told the French news agency AFP.
"There's no water, no milk, there are very few cans -- and no cat food."
Category Five hurricanes are rare. They can tear off roofing, shatter windows, uproot palm trees and turn them into projectiles that can kill people.
In Puerto Rico, Governor Ricardo Rossello activated the National Guard and announced the opening of storm shelters able to house up to 62,000 people.
A US aircraft carrier with a field hospital and dozens of aircraft able to conduct rescue or supply missions have been positioned in the area, according to Alejandro de la Campa of the Caribbean division of the US Federal Emergency Management Agency.
Sheilyn Rodriguez of Rio Grande, 33, said "I really am scared for my kid," a son who is nine. She was stocking up on batteries, canned goods and ice in case the power goes out.