The ex-Soviet Central Asian nation will hold a presidential election on Nov. 19.
The state security service said in a statement it had detained him at an airport upon arrival from Turkey.
In a separate statement, the prosecutor general`s office said it suspected Tekebayev of taking a $1 million bribe from a Russian investor in 2010.
Tekebayev, who was then a senior member of provisional government, promised the investor he would be able to take over a local telecommunications company, prosecutors said.
Kanybek Imanaliyev, a member of parliament who belongs to Tekebayev`s Ata Meken faction, said he denied any wrongdoing.
"He considers his detention... unwarranted and illegal and a continuation of political repressions," Imanaliyev said. "We planned to hold a party congress within a month and nominate him as candidate (for presidency)."
Atambayev cannot run for re-election under the Kyrgyz constitution, but his allies in parliament successfully pushed through a referendum on a package of amendments significantly boosting the powers of the prime minister.
This has prompted speculation Atambayev may either become a powerful cabinet head - although Atambayev denies having such plans - or install a loyal figure as prime minister in order to retain power in the mostly Muslim nation of 6 million.
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