An operation to rescue passengers has been launched by the navy and police. The boat had left the city of Dar es Salaam earlier in the day.
The navy said the vessel, the MV Skagit, got into difficulty because of strong winds.
A minister in Zanzibar quoted by AFP news agency said so far 12 dead bodies had been recovered.
Last September, nearly 200 people died when an overcrowded boat with 800 people aboard sank off Zanzibar.
The MV Skagit left the mainland at 12:00 local time bound for the main island of the semi-autonomous archipelago.
The journey usually takes about two hours.
Thirty-one children are believed to have been on board.
A safety officer at the Zanzibar Port Corporation told Reuters news agency the ferry was now “bottom-up”.
“Twelve dead bodies and 10 survivors have been recovered so far. Rescue operations continue in bad weather,” Mwinyihaji Makame, state minister in the Zanzibari president’s office, told journalists, AFP reports.
The route between Dar es Salaam and Zanzibar is a busy crossing, popular with both Tanzanians and foreign tourists.
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