The typhoon packed gusts of up to 216 kilometres per hour with torrential downpours, forcing the cancellation of hundreds of flights.
In the capital Naha, traffic lights went off and television footage showed trees split by the force of the storm, signboards flying around and a restaurant destroyed, with the shattered building blocking a street.
The coastguard and local police said a 62-year-old man was found dead after he was knocked off his boat in rough waters near Japan's mainland, while public broadcaster NHK said an 81-year-old fisherman died in southwestern Kumamoto prefecture.
Separately, Okinawa police said at least four people were injured, with NHK putting the number of injured at 25.
Schools across the sprawling archipelago were also closed while nearly 70,000 Okinawan households had no power, NHK said.
"We have no water or electricity, but the gas is still on," said Takuro Ogawa, who lives in Chatan, a town in central Okinawa.
Late Monday, the Japan Meteorological Agency issued its highest typhoon alert for Okinawa's main island, home to around 1.2 million people, as well as the outlying Miyako islands. The alerts for the Miyako region were downgraded Tuesday evening.
Authorities had warned there was a risk to life, as well as major property damage from the typhoon and subsequent flooding and landslides.
Officials called on 590,000 people across Okinawa to take shelter in their homes or evacuate to community centres and town halls.
"We have urged residents to evacuate when they see any danger," a local municipal official told AFP by telephone.
More than 700 people have taken refuge in shelters, Jiji Press agency reported, as the powerful storm barrels toward the Japanese mainland.
Neoguri comes less than a year after Typhoon Haiyan, packing the strongest winds ever recorded on land, left more than 7,300 people dead or missing as it tore across the central Philippines in November.
Japan, a wealthy nation with strict building codes, has a strong track record of coming through major storms comparatively unscathed in the last few decades compared to its poorer neighbours.
Nonetheless, Japanese officials are urging people to take the threat posed by Neoguri seriously.
"There are fears about violent winds, high waves and tides and torrential rain that we have never experienced before," Satoshi Ebihara, the Japanese weather agency's chief forecaster, told an evening news conference Monday.
"We are in an abnormal situation where serious danger is imminent," he said.
The World Meteorological Organisation said Neoguri was not as powerful as Haiyan, but that "its impact is not to be underestimated".
"It is expected to remain at strong intensity for the next three days at least," spokeswoman Clare Nullis told a UN briefing in Geneva.
US Astronaut Reid Wiseman posted two dramatic views of the swirling typhoon from the International Space Station with the images from his Twitter account re-tweeted more than 5,000 times.
The Kadena Air Force Base, the biggest US Air Force base in the Pacific which is located on Okinawa's main island, evacuated some of its aircraft as the storm approached.
The typhoon, which has been downgraded from super typhoon status, was in the East China Sea as of 8.50pm (6.50pm Thailand time). It was moving north at about 30 kilometres per hour, the weather agency said.
The storm could reach the southern main island of Kyushu late Wednesday or early Thursday, with the weather agency warning that the amount of rainfall by Thursday could reach as much as 400 millimetres, posing a serious risk of landslides and flooding.
Kyushu — next to the main island of Honshu, where major cities including Tokyo and Osaka are located — was already experiencing heavy rain.
Japan urges thousands to evacuate as a powerful typhoon hits Okinawa with torrential rain and high winds. (Reuters video)