Tens of thousands of revellers will be forced to find alternative routes to the site in Pilton, Somerset.
Great Western Railway (GWR) is operating just five services from London Paddington to Castle Cary on Thursday, with a total of 24 between Wednesday and Friday.
Before the industrial action was announced, 51 trains were expected to run on the route over the three-day period.
GWR told passengers: “We plan to maintain timetabled trains between Castle Cary and London Paddington throughout the course of the Glastonbury Festival.
“Some services might be subject to alterations to train times and we will be in contact with customers who have already booked seats on board those trains.”
It added: “Other parts of the GWR network are likely to be more affected by the strike action and customers may need to consider alternative ways to travel to a station serving Castle Cary.”
Rail strikes are being held across Britain on Tuesday, Thursday and Saturday, but their effects mean services will be disrupted from Monday night until the end of the week.
Roads serving the Glastonbury Festival will be exceptionally busy, with motoring groups advising drivers to avoid the region if possible.
It comes as motorists are being warned to expect a surge in traffic as train passengers switch to road transport during the rail strikes.
The AA predicted that the worst affected roads are likely to be main motorway arteries, as well as rural and suburban areas.
Drivers in Scotland and Wales are expected to face long queues as most railway lines there will be closed during the industrial action on Tuesday, Thursday and Saturday.
The M74, M8 and A9 in Scotland and the M4, A55, A5, and A483 in Wales could see severe traffic, according to the AA.
An AA route planner spokesman said: “Even though the strike is for three days, many travellers will give up on the trains for the whole week.
“It coincides with big events like Glastonbury and the Goodwood Festival of Speed, so drivers not going to those locations are advised to give the areas a wide berth.
“Generally we predict a big increase in traffic in Scotland, Wales and major routes across the UK.
“The impact will be slightly cushioned by record fuel prices deterring some and more commuters deciding to work from home but congestion will still be a problem.”
RAC spokesman Rod Dennis said the strikes will “inevitably lead to the roads being used more”.
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