The new campaign began when the group put up a series of posters overnight on Monday on the main island of the semi-autonomous Indian Ocean archipelago.
The posters read simply 'The Solution is Khilaffa'. The slogan refers to the group's aim of creating a worldwide caliphate - or Islamic state - led by a single Islamic leader.
"We are part of the international alliance calling and believing that Muslims should be led by one caliphate," Chande Khamis, a member of the group, said in Zanzibar's business district on Tuesday.
Zanzibar is 95 per cent Muslim, and its ties with mainland, mainly Christian, Tanzania have been strained in recent years.
During elections in 2000 and 2005, there was widespread rioting in Zanzibar after allegations of vote-rigging by the ruling party.
"Democracy is the way of infidels, and we do not want it to be imposed on the Muslim society," Khamis said.
The archipelago's government is secular and does not endorse any religion.
Hizb ut Tahrir aims to become a global Islamic movement
Under the deal that founded modern Tanzania in 1964 through a union of the islands and mainland Tanganyika, Zanzibar retains its own president and parliament.
Khamis told Reuters the group - whose size he refused to give - does not advocate violence.
"We want to lead peaceful transition from a secular state to an Islamic state," he said.
"We knew the existence of the group but it is for the first time that we see them doing flyers," Juma Khatib Suleiman, the commander of Zanzibar's urban regional police, said.
This was the first time the group had come out in the open and its activities were under investigation, he said.
Britain considered banning Hizb Ut Tahrir in August 2005 after the July 7 London bombings in which four Muslims killed themselves and 52 others, but later backed off without giving a reason.
Hizb ut Tahrir is a worldwide party founded in 1953, and much of its membership is believed to be underground after being banned in several Arab countries including Egypt and Syria, and in Russia.
Western analysis fear that a takeover in Zanzibar by radical Muslim groups could give militants a strategic toehold off the coast of east Africa - already a victim of al Qaeda bombings in 1998 in Tanzania and Kenya.