Some festival-goers have faced delays of up to 12 hours with heavy traffic reported on all major routes to the Somerset site.
Police are advising those planning to take their car, caravan or campervan to Glastonbury to either travel later in the day or put off their journey until tomorrow (Thursday).
Drivers who are already on the road, meanwhile, have been urged to find somewhere safe to stop and wait until the traffic congestion has eased before continuing their journey.
The congestion has prompted the police to call on motorists to avoid travelling in the area unless their journey is “absolutely necessary”.
A spokesman for Avon and Somerset Police said vehicles waiting to get into the site near Pilton have been left queuing back along the A361.
Heavy traffic has also been reported on the A37, to both the north and south of its junctions with the A361 and on the A39.
A four-vehicle accident on the westbound carriageway of the A303, meanwhile, brought traffic to a standstill and prompted Wiltshire Police to advise drivers to seek alternative routes.
To help ease the congestion, a temporary holding site for caravans and campervans has been set up at the Bath and West Showground, the spokesman added.
Those stuck in the queues to get into Glastonbury, meanwhile, are asked to stay in their vehicles so that further delays are not caused when the traffic does start moving again.
Festival organiser Emily Eavis has apologised for the delays and says staff are doing all they can to get music fans into the site as soon as possible.
In a bid to combat congestion, organisers had called on motorists with a spare seat in their car to offer a lift to another festival-goer through the GoCarShare website.
Up to 180,000 people are expected to attend the festival, whose headline acts include Coldplay, Adele and Muse.
Although the gates opened to festival-goers today, the entertainment does not begin at Worthy Farm until Friday.