The storm was located about 595km south-southwest of Bermuda. It had winds of up to 165km/h and was moving north-northwest at 15km/h.
Lee was expected to pass just west of Bermuda, prompting forecasters to issue a tropical storm warning for the island.
"I cannot stress enough that we must all take this storm seriously," David Burch, acting national security minister, said in a press conference.
Bermuda's government announced it would shutter its airport on Thursday and reopen it on Friday. Banks, city parks and ferry service also were scheduled to shut down while public schools would shutter on Thursday and on Friday.
"We don't want 4000 little people wandering around the country in tropical storm winds," Burch said.
Lee is expected to grow in size and keep travelling north as it slowly loses strength in cooler waters. It is forecast to approach the coast of New England and Atlantic Canada on Friday and Saturday and remain a "large and dangerous hurricane," according to the National Hurricane Centre.
A hurricane watch was issued from Stonington, Maine to the US-Canadian border. A tropical storm watch was issued for a large swath of coastal New England from Watch Hill, Rhode Island to Stonington, Maine, including Block Island, Martha's Vineyard and Nantucket. A storm surge watch was issued for Cape Cod Bay and Nantucket.
"Due to Lee's large size, hazards will extend well away from the centre, and there will be little to no significance on exactly where the centre reaches the coast," the NHC said.
Hurricane-force winds extended up to 185km from Lee's centre, and tropical-storm-force winds extended up to 390km, the NHC reported. It warned of wind, rain and coastal flooding for parts of New England and Atlantic Canada.
The storm is approaching as New England struggled on Wednesday with flooding from unusually heavy rainfall unrelated to the hurricane that prompted the governor of Massachusetts to declare a state of emergency.
Forecasters warned of dangerous surf and rip currents in Lesser Antilles, the British and US Virgin Islands, Puerto Rico, Hispaniola, the Turks and Caicos Islands, the Bahamas, Bermuda and the US east coast. The conditions were starting to reach Atlantic Canada.