Donna Kennedy-Glans, member of the legislature for Calgary Varsity, cited the inability to create change from within the party and a culture of entitlement as reasons for her departure.
But she did not criticize Redford by name.
"This is not just about leadership," Kennedy-Glans told reporters in Calgary. "This is about how our party functions and whether change from within is possible.
"We've had conversations about the premier's leadership for months now. I am just one person. I have to make my choices. I'm not here to bring down anyone."
Kennedy-Glans was the associate minister for electricity and renewable energy. She will sit as an Independent.
Redford has been facing increasing unrest within her caucus, fuelled by concerns over her leadership style and a $45,000 trip to South Africa.
Last week, Calgary backbencher Len Webber also quit the Tory caucus, calling Redford a bully and "not a nice lady." On Friday, the president of a Progressive Conservative riding association in northeast Edmonton said Redford must resign or the party will lose the next election.
Kennedy-Glans, who is a lawyer, co-authored a book on how companies can act with integrity. She said in a news release Monday that she was looking forward to putting her beliefs into practice as a government member.
She said that she supported issues discussed during the last election such as a more open and transparent government and one "free of entitlement."
"Definitely there's an issue about a culture of entitlement and we've seen that over the past few months and I hear it at the doors all the time," she told reporters. "People don't like a culture of entitlement. They're egalitarian in Alberta. They want this to stop."
Kennedy-Glans was one of the ministers grilled by the Opposition in the house last week for taking a government plane ride from Grande Prairie, Alta., after a Tory fundraiser. The Wildrose has used the trip as an example of misuse of government aircraft.
The premier met with her caucus Monday morning in Edmonton. Redford emerged afterwards offering no comment on Kennedy-Glans's resignation.
None of her other caucus members crossed the floor Monday, despite an ad hoc meeting of 10 of them on Sunday to discuss, among other options, sitting as Independents.
Finance Minister Doug Horner, asked by reporters about the Sunday meeting, said: "I don't know much about what they talked about, but you're either a part of the team or you're not and I'm pretty cut and dried that way."
The unity was reinforced during question period, when NDP Leader Brian Mason asked Redford, with her 12-year-old daughter in the public gallery as part of a class trip, a question: "Do you have enough support to keep governing?"
All of Redford's caucus members rose in response to give her a standing ovation.
At the same time, all 17 members of the Opposition Wildrose party also stood and cheered Redford — further evidence that she is the one they want at the PC helm when voters go to the polls in 2016.
Monday's caucus meeting came after Redford took questions from PC party executives on the weekend.
Redford was given a "work plan" by the party for moving forward, though neither she nor party president Jim McCormick would say what that meant. McCormick said there was a "wide-ranging, no-holds barred discussion" and the premier's expensive trip to South Africa for Nelson Mandela's funeral came up.
Late Monday, McCormick issued a statement saying the party is "very closely watching the situation" and calling it "a very fluid time."
He said the party would be seeking the guidance and input of its supporters in the weeks and months ahead.
Kennedy-Glans wouldn't say whether she thought other caucus members would follow her.
"Quite frankly this is a personal decision," she said. "If others choose to cross the floor, it's a very significant decision and I certainly do not intend to lead a parade across the floor."
She also declined to say whether she thought Redford should step down.
"I don't know if the premier should resign. I think that's up to her."
— With files from Dean Bennett in Edmonton
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