Around 25 used Covid-19 tests were reportedly given to students in the Selly Oak area on Tuesday.
Birmingham City Council has said the incident involving their distribution service is being “reviewed”.
The tests were handed out as part of their drop off and collect service to help tackle coronavirus cases.
Sophie Dunne, a second year student at the University of Birmingham told the university newspaper Redbrick, that several students left their accommodation to alert council workers about the used tests.
The reports emerged after another second year student said on a community Facebook page that people in high-vis jackets had handed out testing kits that were already “sealed and snapped”.
According to Redbrick, students also said some of the tests had “people’s names and addresses on the tests bags”.
A statement from Birmingham City Council said: “We are aware that a small number of tests were mistakenly given out during Drop and Collect activity in Selly Oak yesterday.
“As soon as it became apparent that the wrong tests had been given out steps were taken immediately to rectify the mistake.
“Drop and Collect is a vital part of helping to tackle the spread of Covid in our City, with 100,000 tests being undertaken to date.
“The circumstances around this incident are being fully reviewed and any required changes to process will be implemented.”
The Drop and Collect scheme involves military personnel providing extra capacity for the council’s door-to-door coronavirus testing service.
It comes as the latest data on weekly coronavirus rates revealed Birmingham recorded 1,911 new infections in the seven days up to October 10, a rate of 164.7 cases per 100,000 people.
This was up from a rate of 154.9 infections per 100,000 people in the previous seven days up to October 3.
Birmingham is a Tier 2 area of the country which means households are not able to meet indoors.