Anne Marie Waters, a former Labour activist and founder of the Sharia Watch pressure group, has previously called Islam "evil".
Her leadership bid has split the party, with some MEPs threatening to quit if she was allowed into the race.
But the UKIP National Executive Committee, which vets all would-be candidates, has allowed her to stand.
The other candidates to replace Paul Nuttall - who stood down after UKIP's poor performance in June's general election - are:
Voting papers will be sent to party members over the next few weeks and the new leader will be announced at the party's annual conference in Torquay on the 29th and 30th of September.
Ms Waters's leadership bid was backed by former English Defence League leader Tommy Robinson and she has previously been blocked from standing as a UKIP election candidate.
James Carver, UKIP West Midlands MEP, said he "sincerely hoped" Ms Waters did not win - but added that she should be allowed to stand.
He said: "Her train of thought, I think is going about it the wrong way... there are many British Muslims in this country and that is a good thing."
The party's former leader, Paul Nuttall, has previously said her views made him "uncomfortable".
Ms Waters believes her anti-Islam message, including a proposed ban on the burka, the closure of all sharia councils and a temporary freeze on all immigration, will strike a chord with many voters.
She has argued that UKIP could regain support if it had the "guts" to be "honest about Islam" and challenge the view that it had "nothing to do" with jihadist violence.
Last month, former leader Nigel Farage told BBC's Sunday Politics that "if UKIP goes down the route of being a party that is anti the religion of Islam, then frankly it's finished".
An anti-Islam candidate has been allowed to stand for the UKIP leadership.