Rows between rival electoral commissioners had led to physical fights, Jecha Salum Jecha said.
The opposition says the vote on the islands was cancelled because it won.
The main challenger in the national presidential election, Edward Lowassa, said the problems in Zanzibar could be mirrored across the country.
Earlier, he called for the national electoral commission to stop releasing results, alleging the whole process nationwide had been marred by fraud.
The elections in Tanzania are the most competitive in the country's history, with four opposition parties forming the Ukawa coalition to challenge the ruling CCM's 54-year grip on power.
Previous elections have turned violent on semi-autonomous Zanzibar, whose two main islands are Unguja, often referred to as Zanzibar, and Pemba.
Mr Lowassa urged his supporters to remain calm and not to engage in street protests.
In his statement, Mr Jecha accused Zanzibari electoral commissioners of being partisan.
More votes had been cast in some areas than the registered number of voters, especially in Pemba, where some party agents had been ejected from polling stations, Mr Jecha said.
The ballot papers for the national presidential election have been taken to Tanzania's main city Dar es Salaam, where they will continue to be counted.
It is unclear if and when new elections for Zanzibar's president and parliament will be held.
Analysis: Sammy Awami, BBC News, Zanzibar:
Never before has an election in Zanzibar - a popular tourist destination - been scrapped. So we are entering uncharted waters.
And yet, this election - unlike previous ones - has not been marred by riots and violence.
There was, however, some tension, which led to the closure of roads and businesses.
On Monday, the main opposition candidate for the post of Zanzibar president, Maalim Seif Sharrif Hamad, declared himself the winner.
His announcement attracted sharp rebuke from the governing CCM party, which called it illegal and a threat to the archipelago's stability.
But life was returning to normal when the archipelago's electoral commission chairman made the shock announcement that he was scrapping the poll because it was full of gross irregularities.
At that point results from 36 of the 54 constituencies had been released.
More on Zanzibar
Tanzania's tightly contested election:
Could CCM lose?
Money, power and politics

Former civil servant Sir John Chilcot will appear before MPs on the Commons Liaison Committee on 18 October.
The report, which took seven years to complete, criticised Tony Blair and his government's case for going to war in 2003.
Mr Blair defended his actions, saying military action had been justified.
The Chilcot Inquiry, which began its work in 2009, after UK troops left Iraq, did not attempt to reach a verdict on the legality or otherwise of the military action.
Mr Blair has continued to insist the decision to remove Saddam Hussein was justified, although he has acknowledged that the intelligence on which it was based was flawed.
Appearing before a separate committee of MPs last month, Cabinet Secretary Sir Jeremy Heyward said he and other civil servants were in the "preliminary" phase of learning lessons from the report in terms of how government should operate in future.
He said he was frustrated at the length of time the inquiry had taken but believed that it could not have been expedited without changing the large terms of reference or restricting access to vital declassified documents and other material.
The liaison committee, made up of the chairs of individual parliamentary committees, is best known for questioning the prime minister of the day two or three times a year.

Miriam Briddon died after the collision involving her Fiat Punto and a Volkswagen Golf driven by Gareth Entwhistle near Ciliau Aeron.
Entwhistle, 34, from the Aeron Valley, admitted causing death by careless driving while under the influence of alcohol on 29 March, 2014.
He will appear again at Swansea Crown Court at the end of July.
The crash victim was a former Ysgol Dyffryn Teifi pupil, described by her family as a "creative person who would be truly missed".
Elections in Zanzibar have been annulled for not being free and fair, the electoral chief on the Tanzanian archipelago has announced.
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MPs will question the chairman of the Iraq War Inquiry later this month for the first time since it published its official report in July.
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A Ceredigion man has pleaded guilty to drink-driving and causing a crash which killed a 21-year-old woman.