The opposition is angry because the draft constitution makes few major changes to the structure of government, claiming it has therefore rejected its calls for a strengthening of the federal system to limit presidential powers.
"I can confirm April 30 as the date for referendum," Attorney General Frederick Werema said.
Opposition lawmakers led by the Chadema party stormed out during debate on the draft, leaving discussion to the ruling Chama Cha Mapinduzi (CCM) party, which has been in power since independence in 1961, and controls two-thirds of the assembly.
If passed, the proposed constitution would come into force ahead of general elections due in October 2015. However, President Jakaya Kikwete has served his two terms in power and cannot run again.
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In 2011, the government agreed to draft a new constitution, with a team touring the country to collect ideas. But critics say those suggestions were not properly reflected in the draft.
"The whole process was not only a waste of time but also a waste of resources," said Chris Maina Peter, law professor at the University of Dar es Salaam.
It would also grant women equal land ownership rights.
A new constitution would also impact the autonomous government in Tanzania's Zanzibar archipelago, amid calls by some islanders to end to the 50-year union with the mainland.