The chicks worth about $6,000 were impounded on Monday at the northern Namanga border post before being set alight on Tuesday.
The Tanzanian government banned the importation of chicks in 2007.
Arusha-based businesswoman Mary Matia who had imported the birds was taken into police custody.
Veterinarians in Tanzania have condemned the country's s decision to burn to death 6,400 chicks which had been imported from Kenya illegally.
The chicks worth Tsh12.5 million (about $5,570) were impounded on Monday at the northern Namanga border post before being set alight on Tuesday.
Tanzania Animal Welfare Society executive director Dr Thomas Kahema said there were other alternatives to curb outbreak of bird flu.
He said the 2008 law on animal welfare guarantees the protection of the chicks and that it was cruel to burn them.
Further Dr Kahema said the authorities could have been sent the newly-hatched birds back to Kenya since they had not verified that the chicks had been infected.
"The decision distorts the country's image as one that does not respect animal rights," he said.
Other Tanzanian animal rights enthusiasts also expressed their discontent with the burning of the chicks saying it was cruel.
The government veterinary official for the Northern Zone, Mr Obedi Nyasebwa, had said Tuesday that the aim was to curb the outbreak of bird flu.
Further, he said the government had banned the importation of chicks in 2007.
Arusha-based businesswoman Mary Matia who had imported the birds was taken into police custody.
Tanzania Revenue Authority assistant manager at the Namanga border Mr Edwin Iwato said the owner of the vehicle that carried the chicks would also be fined.
Senior veterinarian Medard Tarimo said complaints about chick smuggling had been rife.
“They are mostly smuggled at night, endangering the health of Tanzanians since we know avian influenza has broken out in neighbouring Uganda.”
