Video footage showed Ms Leadbeater, the sister of murdered MP Jo Cox, being shouted at by a man believed to be protesting against LGBT education in school.
In response to the abuse, Ms Leadbeater said: "This is where I live, this my community. Don't come here and shout me in the street.
"The Muslim community in Batley deserve better than this."
Ms Leadbeater then turned to walk away from the scene, while the man shouted: "Do not walk away, do not walk away."
They then chased the candidate to her car.
It is believed the protestor is not from Batley, but is a long-standing opponent of LGBT education who had travelled to the West Yorkshire town to heckle Ms Leadbeater.
Speaking after the incident, Kim Leadbeater said: "Is it any wonder that people, particularly women, don’t want to enter politics when stuff like this happens.
"For my family and friends to see this has caused a huge amount of distress. I’ve spent the last few years working on civility in public life and today shows why that work is more important than ever.
"This isn’t the first time I’ve been shouted at in the street during the campaign and I’m very happy to take part in robust political debate but when that turns into intimidatory behaviour, I hope we can all agree a line has been crossed.”
After the incident, Ms Leabeater told Byline Media that fellow candidate George Galloway was across the road laughing at her at the time, something he refutes.
Mr Galloway tweeted: "The extremist who harassed my Labour opponent today has I’m told previously been thrown out by my security from one of my public meetings. He is a provocateur."
He later told the Yorkshire Post: "It’s entirely untrue. An unevidenced desperate smear. I utterly condemn what happened."
Labour MPs have united in support of Ms Leadbeater's handling of the abuse.
Leader Keir Starmer said: "The abuse Kim Leadbeater has faced is disgraceful. George Galloway’s poisonous politics have no place in our country. The best way people can counter it is by voting for Labour and Kim next Thursday."
Barnsley MP Dan Jarvis tweeted: "Repugnant and totally unacceptable behaviour directed at Kim. She should not have to put up with this, but as ever she displays her decency, dignity and indefatigability in standing against this bile."
And Alison McGovern, MP for Wirrall South, said: "Honestly Kim Leadbeater is the bravest of the brave. The very very best of all of us. People telling me they had already voted for her (by post) this week was so uplifting. She would be a phenomenal voice for Batley and Spen. Do not give in and do not give up."
The by-election will be held on Thursday July 1.
Other candidates include Ryan Stephenson for the Conservative Party.