The party leader was apparently with his wife and two younger children at the Queen's Head in Downe, Kent, when the incident took place.
Dozens of demonstrators initially went into the George & Dragon, where Farage has previously been pictured having a drink, before realising he was in the other pub nearby.
Using the hashtag #ukipcon, they posted images of the event, including one that apparently showed Farage leaving.
— P4SRE (@P4SRE) March 22, 2015
They are said to have gone into the Queen's Head, chased the Farages out and then jumped on the Ukip leader's car bonnet as he drove away.
Farage said afterwards: "I hope these 'demonstrators' are proud of themselves. My children were so scared by their behaviour that they ran away to hide.
"At the time of writing this a relative has gone to look for them, and they are not yet at home. These people are scum."
Farage's children are now understood to have been found and returned home.
His children with current wife Kirsten are Victoria and Isabelle, thought to be aged 15 and 10 respectively. He also has two grown up children from his previous marriage.
Staff at the Queen's Head refused to comment on the episode, while the George & Dragon said protesters had initially claimed they were there for a birthday party.
The story continues below the pictures
Protest organiser Dan Glass said the group was in fancy dress and included migrants, HIV activists, gay people, disabled people and breastfeeding mums.
The demonstrators said Farage had pushed through to get into his car, and was then chased down the road, with some people jumping on the bonnet of his car.
Ukip is understood to have requested taxpayer-funded security for Farage during the election campaign amid fears that he is regularly being targeted by protesters.
In a statement, Glass said: “UKIP are a con. They pretend to be anti-establishment but this couldn't be further from the truth. By wrongfully shifting the blame for the economic crisis onto immigrants they have let the bankers off the hook.
"That is why so many diverse communities have taken our cultures to the heart of where they exist - Nigel Farage's local pub. We will not succumb to their prejudice. We will create the world we want to live in. A world beyond UKIP.
"We sympathise with people who feel alienated with the political system but a vote for UKIP really is the worst thing you could do to protest about the current state of this country.”
Responding to reports that Farage's children had fled from the protest, Glass said: "He was sitting on his own and left on his own. We didn't see any kids".
The organisers of the protests later released a statement attributed to "photographer" Mike Kear.
"As some protestors and the press entered the rear of the pub, I saw a blonde haired woman leaving with two children," it said.
"At the time, the scene was calm although she seemed very keen to get out of the pub, possibly not wanting them to be identified. At no time were any children seen to be scared or running away.
"Could this be that Farage is manipulating the truth for his own ends?"