Ms Williams - a campaigner against drink driving - admits having "several glasses of wine" before crashing her car into a tree east of Brisbane on Thursday night.
Police are investigating the incident and no charges have been laid.
The mayor is resisting growing calls from constituents and state and federal politicians for her to resign.
Local mother Judy Lindsay, whose daughter Hayley was killed in a crash involving a drink-driver in 2009, has started a petition calling for Mr Williams' dismissal.
About 1300 people had signed the petition on the state parliament website by Tuesday afternoon.
"Queensland residents draw to the attention of the House that the people of Redlands have lost confidence in the Mayor," the petition said.
"Your petitioners, therefore, request the House to call upon the Minister for Local Government to dismiss Redland City Council Mayor Karen Williams."
A second petition has also been started on Change.Org calling for the mayor to resign or be sacked.
"I can not see how the community can accept this and allow Karen to remain in her position of Mayor," said organiser Rick Young.
"If you believe Karen Williams should resign or be stood down. Sign this petition."
AAP has sought comment from Ms Williams.
Redland council chief executive Andrew Chesterman said on Monday it was an "upsetting time" for many council employees "who work every day to make our city a better place".
He said the crash had occurred after a "small post-budget thank you event", and noted that no charged had been laid in relation to the accident.
Hours before the crash Ms Williams had hosted an online meeting with Ms Lindsay and two other families whose loved ones had been killed in accidents caused by drink-drivers.
She said the mayor then rang her in tears on Friday night to apologise.
"I just said I can't have any contact with you any more. You can't be doing the job you're doing. I trusted you and this is what you've done," Ms Lindsay told Nine's Today program on Monday.
"She's got to go. She has no respect for anybody in this community by doing what she's done."
Queensland Opposition Leader David Crisafulli said his Liberal National Party colleague should face consequences for her actions.
His federal counterpart Peter Dutton and Nationals leader David Littleproud also called of Ms Williams to resign.
Premier Annastacia Palaszczuk refused to be drawn on the mayor's future but did say it was very serious - particularly for someone who has campaigned against drink driving.
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