Babacan, a founding member of the Justice and Development Party (AKP), cited "deep differences" over policy and said Turkey was in need of a "new vision", in a statement criticising the government's direction.
The markets viewed the popular liberal politician as a guarantee of sensible economic policies during his time as economy minister between 2002 and 2007.
"In the last few years, deep differences have arisen between the approach taken in many areas and the principles, values and ideas I believe in," Babacan said, according to HaberTurk website.
"Under the current circumstances, a brand new vision for the future is needed for Turkey," he said, calling for "new strategies, plans and programmes".
His official page on the AKP website as a "founding member" was no longer available.
There has been fevered speculation that Babacan will set up his own political party and some local media reported other AKP MPs could leave to join him.
Babacan appeared to confirm the rumours, insisting a "new effort" was "inevitable" for Turkey's future.
"I and many of my friends feel a great and historical duty to start this effort," he said, adding that as a result, he could no longer continue as an AKP member.
Turkish media has reported that Abdullah Gul, former president and co-founder of the AKP, could be part of a new party under Babacan.
Abdulkadir Selvi, a pro-government columnist in the Hurriyet daily, wrote last week that Babacan met Erdogan on May 30 with the intention to resign but decided against quitting the party so close to the Istanbul mayoral election of June 23.
Selvi said Babacan told the president he was planning to resign and admitted he was setting up a party.
The AKP lost a re-run vote in the country's biggest city last month by more than 800,000 votes after an initial defeat on March 31.
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