Maria came ashore around 8:30 am (2330 GMT Sunday) near Ofunato city in Iwate prefecture, the Japan Meteorological Agency said.
It was initially categorised as a "severe tropical storm", one level below a typhoon, but was downgraded to a "tropical storm" by Monday afternoon as it lost some of its strength.
There were no reports of injuries or severe structural damage, according to the Iwate Prefecture government.
Two families were trapped inside their houses in a remote town due to an overflowing creek, the Iwate government said.
The region's municipalities issued evacuation advisories and warnings to some 315,000 residents overnight, and around 2,000 people spent the night at local shelters.
The storm dumped 368 millimetres (14 inches) of rain in the 24 hours to Monday morning in Kuji city, the most since the meteorological agency began keeping records there in 1978.
The area's average monthly rainfall for August is 177.9 millimetres.
The city also issued an urgent evacuation warning to about 8,300 residents living along a river as a nearby dam began a controlled release of water to prevent overflowing.
"The residents in the affected region are advised to be vigilant about landslides, surging and flooding rivers and flooding in low-lying areas, as well as violent gusts and high waves," the weather agency said.
Some 300 households in Iwate were without power Monday afternoon, according to regional utility Tohoku Electric Power.
As of noon local time on Monday, Maria was travelling above Hanamaki city in Iwate, bringing gusts of up to 108 kilometres (67 miles) per hour and moving northwest at 20 kilometres per hour, the agency said.
It has forced the cancellation of flights to the northern region. Japan Airlines said it cancelled 78 domestic flights, affecting 7,039 passengers. Its rival ANA cancelled eight flights, national broadcaster NHK said.
Some regional train services suspended their services, although the bullet train system continued its normal operations.
The storm was expected to cross Japan and head out to the Sea of Japan by Monday evening.
Scientists say climate change makes extreme weather such as heavy rains and tropical storms more frequent and intense.
hih/tym
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