Woolfe was excluded earlier today following a vote of Ukip's National Executive Committee, after he submitted paperwork for his entry 20 minutes after a midday deadline.
Banks, the party's most high-profile donor - who was also backing Woolfe's leadership bid - has said the decision is "bleak news for Ukip".
Speaking to City A.M., Banks said: "[Woolfe] was the leading candidate, so to exclude him because of a computer glitch on a website is insanity."
"I like [leadership contender and Ukip deputy chair] Diane James as well very much, but I think this is a bit more fundamental in terms of where Ukip goes from here. The Conservatives wouldn't have excluded Theresa May if she'd had computer problems. It's crazy."
Banks added the verdict increased the prospects of him seeking to create a distinct political party.
"We have been looking at whether a new party should start, which bits we might want to keep and what is the best way of doing things. This has to make that more likely, because [the NEC] has just shown that they are not capable of running Ukip," he said.
Woolfe has yet to respond to the announcement.