Ms Munt said it was "with regret" she had quit, but she would not compromise on her opposition to fracking.
The Wells MP defied the party whip to support a rebel amendment seeking a moratorium on shale gas extraction.
She had initially said she would remain in her role despite breaching collective ministerial responsibility.
However a spokesman for Mr Cable later confirmed that she had quit as his aide.
Ms Munt said it was clear her views "cannot be reconciled with the government on this matter" and she would "continue to campaign vocally" against fracking.
Mr Cable's spokesman said: "Both the secretary of state for business [Mr Cable] and the deputy prime minister [Nick Clegg] thank Tessa for the work she has done in government but understand her strength of feeling on this issue and have, therefore, accepted her resignation."
The rebel amendment, which attracted cross-party support, was put forward during a debate on the government's Infrastructure Bill on Monday.
The Commons Environmental Audit Committee had warned there were "huge uncertainties" about the environmental impact of the controversial shale gas extraction technique.
However, MPs overwhelmingly defeated the bid to suspend fracking while an assessment is carried out, by 308 votes to 52 - although the government did agree to 13 new conditions, proposed by Labour, to be met before fracking can take place.
These included the completion of an environmental assessment and the need to consult residents on an individual basis.
A ban on drilling in national parks was another of the suggestions in the Environmental Audit Committee's report.
Ms Munt said she backed the amendment "on principle".
In her initial statement, she said she remained as an aide to Mr Cable, and would continue to campaign against fracking.
A PPS would normally be expected to resign, or face the sack, for voting against the government, as it breaches collective ministerial responsibility.
However, in a statement on Tuesday evening, the Wells MPs said: "I am unwilling to compromise and cannot change my opposition to fracking.
"I will continue to campaign vocally against fracking and as result it is clear that my views cannot be reconciled with the government on this matter."
Lib Dem MP Tessa Munt has resigned as a parliamentary aide to Business Secretary Vince Cable after voting against the government on fracking.