Lan brought high winds and heavy rain as it made landfall around 3 a.m. local time on the Pacific coast of central Japan, the Kyodo News service reported.
Rivers burst their banks in several parts of the country, flooding streets. Video from Japan's public broadcaster NHK shows collapsed roads and homes engulfed by a massive mudslide.
Kyodo reports that Japan Airlines and All Nippon Airways canceled over 100 flights Monday, affecting over 25,000 passengers.
Lan was whipping sustained winds of 165 kph (100 mph) early Monday, according to CNN Meteorologist Haley Brink.
The system will weaken slowly as it tracks quickly to the northeast into the Northwestern Pacific; but will sustain tropical storm force winds of 90-110 kph (57-70 mph) over the next 24 hours, Brink said.
The season's 21st typhoon brought heavy rainfall over much of Japan.
Shingu had received nearly 900 millimeters (35 inches) of rainfall since Friday -- over 500 millimeters (19 inches) falling in just 24 hours, Brink said.
Ahead of the storm, more than 200,000 people had been ordered to evacuate, according to the Fire and Disaster Management Agency, with a further 2.2 million homes under advisory to prepare for evacuation.
In Fukuoka, a city on the southern island prefecture of Kyushu, a 63-year-old man died when falling construction scaffolding struck him, police in the city told CNN.
Police in Osaka, in central Japan, said a woman was found dead in a flooded car in the city, though they could not immediately be certain the incident was related to the typhoon.
The storm had already caused massive waves in South Korea.
Typhoon Lan is so enormous that its cloud field is larger than Japan, Brink said.
On Sunday, Japanese voters participated in a snap general election that put Shinzo Abe on course to become the longest-serving leader in the country's post-war history.
The turnout Sunday was hit by the typhoon, but a record number of Japanese citizens had voted early.