Ms Evans, who is currently suspended from UKIP, said she would "very much like" to run but a "handful of people at the top" had ensured she could not.
Ms Evans' six-month ban for bringing the party into disrepute - claims she has dismissed - means she cannot stand.
She said she would back councillor Lisa Duffy to succeed Nigel Farage.
Ms Evans said UKIP needed to "break free of its hard-right image and set itself firmly in the common sense centre-ground" and also conduct some "internal reform".
The leadership contest has been prompted by Mr Farage's decision to stand down following the UK's vote to leave the European Union, saying his "political ambition has been achieved".
In a statement in Westminster, Ms Evans, who had been touted as a possible successor, said: "I'd very much like to run in that election.
"Unfortunately there are a handful of people at the top of UKIP who, for whatever personal reasons of their own, have made quite sure I can't."
She claimed the party rulebook had been "abused" to suspend her to prevent her from representing the party in May's London Assembly elections and the upcoming leadership contest.
Her six-month suspension handed down in March came after an internal disciplinary meeting found she had publicly criticised a fellow candidate and held herself out as a party spokeswoman without authority.
Ms Evans - who has always rejected the claims against her - lost a High Court bid to overturn the decision.
In the statement, she said: "I have to face up to reality, there's no way they're going to allow me to put my name on the ballot paper... I've now given up hope of becoming the next leader of UKIP."
Ms Evans said she had questioned whether to stay on in a party that "allows, and arguably encourages senior figures to behave like this", but she said the support from members had made her "more determined ever not to give up on UKIP".
She also said that with the right leader, the "sky was the limit for the party".
Endorsing Lisa Duffy, a district councillor for Ramsey in Cambridgeshire, Ms Evans said she was "the best chance" UKIP had to "change, to grow and to thrive".
She said UKIP needed "a clean break from the past" to become more like a political party than "just a rugby club on tour".
Under Ms Duffy's leadership, she argued, the party would be "more united and consensual".
Prior to her suspension Ms Evans wrote UKIP's 2015 general election manifesto. She was axed from her policy role in the party in-fighting which followed Mr Farage's "unresignation" after the general election.
Mr Farage has denied her ban was due to criticism of him.
UKIP ex-deputy chairwoman Suzanne Evans says she has given up hope of becoming the party's next leader - but insists she will not "give up" on UKIP.