A queuing system will be in place at Southampton Central station and supporters will need to join the , externalline and wait for the next available service.
The engineering work will also impact those heading to the London Marathon on Sunday.
Meek said the £1m works had been planned “for a couple of years”.
He said between the football and the marathon about 10,000 people were expected to travel on services to London.
“We are putting on extra trains but from previous occasions when we have done this it is not going to be enough,” he said.
Meek added: “Trains are running via Havant – it’s a long way round so it’s going to be a couple of hours on the train and there will be an awful lot of people trying to get on them.
I would advise people absolutely to seek alternatives.
“The main problem is going to be the return from Waterloo in the evening – that will also depend on any extra time or penalties because that will delay fans getting to Waterloo.”
SWR said those not attending the match and travelling to/from Southampton Central should consider travelling between 1300 and 1900 when trains are expected to be less busy.
