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.

The club wants to develop the former Twelve Oaks Golf Club in Highworth into a training ground and offices.
The Robins' chairman, Lee Power said: "Nigel Eady left a significant sum of money in his will to be invested for the benefit of STFC and the community."
Currently the club leases its stadium from Swindon Borough Council.
Nigel Eady was a lifelong supporter of Swindon Town and bequeathed the undisclosed sum from his will.
DBS Consulting is involved in the project and the ongoing talks between the trust and football club.
Managing director, Les Durrant, said: "Discussions have been going on between the Nigel Eady Trust and Swindon Town because the trust want to invest in it, not just for the football club but also for the wider community.
"The discussions have been around the trust taking ownership of the site and the facilities being developed for the football club to be used."
The former golf club was bought by Mr Power a year go but as yet it has no planning permission.
The hope is to create a new gym, treatment rooms, lecture rooms, grass training pitches and a floodlit 4G artificial surface pitch.
On Wednesday evening, the club met the town councillors to talk through the project.
Mr Power added: "We are working closely with the Nigel Eady Trust and the local community.
"We will be developing our proposals in greater detail after further consultation with local people and clubs/organisations over the next few weeks.
"We want this new training centre and pitch facilities to be of benefit to the local clubs as well as Swindon Town."
The aim is to develop the site over the 24 months.

The move comes as US firm General Electric (GE) and Germany's Siemens vie to take control of French engineering group Alstom's power business.
Any such takeover will now need approval from Economy Minister Arnaud Montebourg.
Mr Montebourg is known to favour the Siemens approach over the GE bid.
In a statement, he said the government's new powers of veto would be "applied in a selective and proportional manner, taking each situation into consideration".
Until now, the French government's power to intervene was confined to deals concerning defence and security matters. The decree extends this to the energy, water, transport, health and communications sectors.
Last week, Alstom reported a 28% drop in full-year net profit to 556m euros ($774m; Â£456m).
The company blamed the fall on restructuring costs, asset writedowns and tough economic conditions.
Alstom is currently considering a $16.9bn offer from GE for its energy business, but Siemens has also shown interest in the unit.
The French firm has said it will decide by the end of May which bidder it prefers.
The power business accounts for about 70% of Alstom's total revenue, and if a deal went through, it would leave the company as a transport business. Alstom's transport unit makes TGV high-speed trains and signalling equipment.
Both GE and Siemens have already met French President Francois Hollande to discuss their potential offers.
The French government has opposed GE's offer.
Heavy downpours have hit train services and left roads in parts of Hampshire impassable.
[NEXT_CONCEPT]
Swindon Town FC hopes to develop new training facilities with the help of money from a trust set up by a former supporter.
[NEXT_CONCEPT]
French Prime Minister Manuel Valls has signed a decree giving the government new powers to block foreign takeover bids for companies deemed "strategic".