South West Trains said the line between Eastleigh and Fareham via Botley had been shut because of flooding.
The B3354 Winchester Road in Botley was also closed after two trees came down, one on to a van - the driver was taken to hospital with a fractured sternum.
Residents in Bishops Waltham and Botley have been warned to prepare for flooding, with more rainfall forecast.
A flood warning has been issued by the The Environment Agency (EA) for the Upper River Hamble area including Durley Mill and Botley Mills.
The (EA) said more than 50mm of rain had been recorded at Bishops Waltham overnight.
Police have urged drivers not to risk driving through floodwater.
Heavy downpours have hit train services and left roads in parts of Hampshire impassable.