Walsall Council leader Mike Bird said the kits posed no risk to anyone’s safety as they were securely sealed when they were put in the wrong place.
And he praised the volunteers who have overcome snow and freezing conditions in the past week to deliver swabs to thousands of people being tested for the South African variant of coronavirus in the WS2 and parts of WS3 areas of the borough.
Councillor Stephen Craddock, cabinet member for health and well-being, visited them to personally apologise and reassure them there was no risk.
He also said procedures had been tightened up to try to stop incidents such as this occurring again in the future.
The test packs come in grey bags and people are asked to complete them, put them in two sealed clear bags before finally placing them in a box provided which will be sent away to a lab.
It appears this error occurred when a resident put the sealed used tests back in the grey bags instead of the box and handed them to a distributor.
Councillor Bird said: “Volunteers over the last few days in the most awful weather have been out there dropping and collecting the testing kits.
“Yes, when you have the human element, sometimes things go wrong. But for the record, while the test was used, it was sealed and had got into the wrong place. There was never at any time a danger to the public.
“The volunteers who have worked tirelessly during the last few days with a task before them to test more than 10,000 people to make sure the community is safe.
“I thank all of the efforts that have gone in from those volunteers and indeed Stephen Craddock, who has had a baptism of fire coming into this cabinet.
“We have been able to motivate and mobilise the people who without which we wouldn’t have been able to tackle the mammoth task we have in the WS2 area.”
The authority started the process of testing 10,000 people aged over 18 last week following the discovery of the new variant.
Two testing sites were set up at Forest Arts Centre in Leamore and Walsall College and the delivery of kits door to door began on February 3.
To date, almost 4,000 tests have been distributed in a week by volunteers and council staff.