Private test results shared with NHS Test and Trace led to 3,853 notifications being wrongly issued on 13 February, the government confirmed.
Employees were told by Amazon the day before they were negative for the virus, then given the exact opposite message by contact tracers.
One test and trace call centre received more than 500 calls from employees.
The company has been testing frontline UK workers privately since October, sending the results to Public Health England, who then share them with NHS Test and Trace and equivalent bodies in Scotland, Wales and Northern Ireland.
Amazon said it had followed NHS instructions and all workers had been made aware of the error and supported to take "appropriate action steps".
The Department for Health and Social care said all employees wrongly issued self-isolation notifications were "rapidly" informed they did not need to.
In messages seen by the BBC, one warehouse worker was told they were negative for Covid-19 on Friday by their employer and then wrongly notified they were positive by NHS Test and Trace and told to self-isolate for 10 days on Saturday morning.
A follow up message from contact tracers confirming a "system error" was sent that evening.
A call centre employee, working for a private company on behalf of test and trace, told the BBC the error led to thousands of confused Amazon employees contacting the 119 helpline.
The call handler, who wishes to remain anonymous, said their team alone received more than 500 calls on Saturday.
They said: "It's not only affected their staff, but the families and households of their staff as well.
"Partners and children of Amazon staff who were added as contacts, told bosses they had to isolate and have lost income."
The Department of Health and Social care said the "vast majority" of people reported no issues with the testing and contact tracing process.
A spokesman said: "Working closely with Amazon, NHS Test and Trace rapidly notified affected employees to let them know they did not need to isolate."
An Amazon spokesman said: "We've communicated with our associates and partners to support them with the appropriate action steps, as instructed by the NHS."