The Indian house crow is notorious for stealing food directly from humans and carrying off valuables such as watches, earrings and even kitchen utensils.
Thousands of the birds have been killed since late August from the use of the chemical DRC 1339, or the Ralston-Purina product Starlicide.
It has been deployed in bait around the capital, Dar es Salaam.
The eradication program is funded by Denmark, Finland and the United States. It will be expanded beyond the capital later this month.
Residents are being told that while the poison is biodegradable, they must be careful not to touch the dead birds or the poison itself.
The Indian house crow has been eradicated in Australia, where it was also imported by ship.