The case was picked up by random sampling of all positive tests at the end of April and the resident is thought to have passed the virus on to two members of their household.
All are isolating and contacts have been traced and tested as a precaution.
It is thought that the person contracted the variant outside of Staffordshire, and there is no evidence that it has spread to the wider community.
It comes after a probable case of an Indian variant of Covid-19 was found in the Black Country.
The case, which was identified in the Sandwell borough, is linked to someone who has recently travelled to India, Public Health England (PHE) West Midlands said.
PHE is working with Sandwell Council to prevent further transmission.
The contacts and movements of the case have been traced and all those who are deemed at risk of infection have been advised to self-isolate and are being offered testing, PHE said.
The Indian variant of Covid-19 is being monitored closely by Public Health England.
Dr Richard Harling, director for health and care at Staffordshire County Council, said: “We have been working with Public Health England to trace all contacts of this case. There has been very limited contact with others outside the household, and these have been thoroughly traced and tested to ensure there is no further spread.
“After tracing all movements and contacts of this case, we believe the variant originated outside of Staffordshire, so this appears to be an isolated case that has not spread to the wider community.
“A small number of people who may have come into contact with the resident while they were infectious are being offered testing this weekend as a precaution and any positive results will be sent to check for the variant.
“This case shows the importance of getting tested regularly. Regular testing allows us to pick up on cases, even those showing no symptoms, and isolate any potential contacts to prevent further spread of the infection.”