The A344 next to the monument was shut in June to "restore the dignity" of the stone circle as part of a Â£27m project.
Residents of villages including Shrewton and Orcheston say their lanes have become "rat runs" for drivers avoiding congestion on the A303.
Campaigners will collect signatures for a petition this weekend.
Janice Hassett, from the Shrewton Traffic Action Group (Stag), said: "The A344 should not have been closed before the A303 was dualled.
"The A303 at Stonehenge Bottom was bad before, but it's a nightmare now.
"Traffic is stupidly backing up to Thruxton on a holiday weekend.
"Sat-navs are sending people right through our villages. There's going to be an accident."
The petition is asking for "urgent action" to be taken to tackle high volumes of non-local traffic using the B3086 through Shrewton, a 20mph speed limit to be introduced and better signage to be installed.

Rikki Evans, 28, started playing the bagpipes at 11:00 on Wednesday and stopped playing more than 24 hours later on Thursday.
Under Guinness rules he was allowed to take a 10 minute break every two hours.
Mr Evans is now awaiting official confirmation from Guinness World Records that he is the new record breaker.

Fleetwood, who won at January's Abu Dhabi Championship, shot a superb nine-under 63 to make up eight shots on Austrian Wiesberger in China.
But the 26-year-old drove into trouble on the extra hole and Wiesberger holed out from five feet for the win.
England's Ross Fisher finished joint third after a bogey on the 18th.
Fisher had seemed set to join Fleetwood and Wiesberger in the shoot-out but his error on the last left him tied with France's Gregor Bourdy on 15 under.
English duo Jordan Smith and Matthew Southgate were the next highest-placed Britons, finishing another four shots back in joint 14th.

The Olympic bronze medallist split the strong Chinese pair of Aisen Chen, who took gold, and Qiu Bo to improve on his bronze-winning performance in Windsor, Canada a week ago.
"There are still things I have to improve, but I'm very happy with the silver medal," said 21-year-old Daley.
"It was fun to battle against Chinese divers to see who can come out on top."
He added on fina.org: "This is the last chance to compete against them before Rio. That's exciting and nice to know that going into Olympic Games I can be very close to the Chinese."
Attention now switches to the European Aquatics Championships in London next month, a key part of Daley's preparations for Rio.
"It will be a very special competition," said Daley. "I live in London, train in London. But it's going to be tough."

Caerphilly council has been accused of lacking "Christmas cheer" by the opposition Plaid Cymru group.
But council leader Keith Reynolds said it has made cuts to protect key services.
The ruling Labour group said the decision was taken "reluctantly" but it had to save £12m for 2015-16.
Plaid's Colin Mann said: "It will be really disappointing if our town centres don't have any Christmas cheer this year with the lighting cancelled."
He said the lighting was available, but there is no money to pay contractors to put up and dismantle it.
People concerned with traffic congestion in villages near Stonehenge are stepping up a campaign for "urgent action" to be taken.
[NEXT_CONCEPT]
A man from Aberdeen hopes to have set a new Guinness World Record by playing the bagpipes for over 24 hours.
[NEXT_CONCEPT]
England's Tommy Fleetwood was denied a second 2017 European Tour title after losing a play-off to Bernd Wiesberger at the Shenzhen International.
[NEXT_CONCEPT]
Great Britain's Tom Daley claimed silver in the men's 10m platform at the Diving World Series in Kazan, Russia.
[NEXT_CONCEPT]
There will be no Christmas lights in towns around Caerphilly county this year after funding was cut.