Organisers said rain and ground conditions had caused delays and urged people "not to set off".
Festival founder Michael Eavis apologised and said: "We did ask people to come in later."
More than 100,000 people are due to descend on Worthy Farm for the event.
The gates officially opened at 08:00 BST but people have reported queuing for more than seven hours to get on to the site.
One ticket-holder told the BBC he had been in the queue for "about four and a half hours" and only moved half a mile.
"We're trying to get in the campervan field but we're glad we've come today because we think it's going to be even worse tomorrow," he said.
Others took to social media to vent their frustrations, with Angela Gibbon tweeting: "7 hours in the queue now...so near yet so far away!".
Steve Saunders posted a shot of the roadside saying: "This is a view of a hedge we've had for a hour. It's a beaut!" while Patrick Dear tweeted: "Talking about necessary survival plans now - which of us to eat first."
Mike Ross said he had "never been on a roundabout long enough to take a nap before" and Moira tweeted that she had "been in this traffic for 12 hours, that's longer than any of my relationships".
Mr Eavis said he was "sorry for the delay" but the problem was because "people were coming before the gates were open".
"We did ask people to postpone their trip by about six or seven hours but instead of that - funnily enough - more people have come early this time," he said.
"I don't mind them coming early but they're going to have to wait because we don't have the staff or the car parks until 8 o'clock in the morning."
Festival organisers have advised people "not to set off" yet or "grab some essentials" if they are on the road as they may have a long wait in their vehicles.
A temporary campervan and caravan holding site has also been set up at the Bath and West show ground near Shepton Mallet and festival-goers are being advised to go there.
Avon and Somerset Police said traffic was queuing on the A37, north and south of the A361 junctions, with further congestion around the A303.
The force has advised people to avoid the area "unless absolutely necessary".
Residents have described the gridlocked roads as a "traffic disaster".
Nigel White, said the A39 through Ashcott was "virtually at a standstill" while Judith Templeman said "no other event would be allowed to cause this level of mayhem".
"If they can't handle the influx of people in an efficient way so as not to cause this level of disruption on all the access routes around Shepton Mallet... then it should be stopped or limited to the number that can be processed efficiently," she added.
Frome MP David Warburton tweeted it had "not been so bad for years" and he would be writing to Mr Eavis as this was "not good for Somerset".
The Met Office posted a weather update on its Twitter account, saying further outbreaks of rain over Glastonbury this morning had added to the "already very wet ground conditions."
Pictures emerged on Monday showing flooding at the Somerset site, with paths under water and camping areas already turned into mudbaths.
Muse, Adele and Coldplay all headlining the main Pyramid stage over the weekend.
Other acts include Jeff Lynne's ELO, Earth Wind & Fire, Ronnie Spector, Art Garfunkel, Madness, Squeeze and New Order.