Some 800 demonstrators have gathered in the town of Bazar Korgon to block the highway that links southern Kyrgyzstan to the country's capital, Bishkek.
Bazar Korgon is Tekebaev's home district.
Dozens of other demonstrators are picketing the regional administration building in Osh, further south.
Protests are also reported in nearby Jalal-Abad.
Tekebaev was arrested at Warsaw airport on September 6 and charged with attempting to smuggle heroin into the country.
Rights activists and opposition supporters say they believe Kyrgyzstan's secret services planted the 600 grams of narcotics that Polish border guards reportedly found on Tekebaev.
Prime Minister Feliks Kulov today said he is "100 percent sure" Tekebaev is innocent and has fallen victim to a "dirty provocation."