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 probable case is the VUI-21APR-01 variant, which is one of three first seen in India which have been detected in the UK and originally designated “under investigation” by PHE.
One of the other three variants has today been elevated to a “variant of concern”.
It comes after three probable or confirmed cases of one of the variants originating in India were discovered in the West Midlands as of April 22, according to Public Health England's SARS-CoV-2 variants of concern and variants under investigation in England technical briefing 9.
Sandwell’s Director of Public Health Dr Lisa McNally said: “Public Health England (PHE) lead on the identification, investigation and communication of new variants of the virus.
"Data on the numbers of new variants in local areas across our region is held by them.
“PHE advise Local Authority Public Health teams on whether surge testing in the wider community is required in relation to new variants. We have not been advised to surge test in relation to the India variant as yet.
"We will of course be ready to deploy testing, or other work such as enhanced contact tracing, as the need arises."
The vast majority of cases of this variant are related to travel, PHE added.
While the VUI-21APR-01 variant has similarities with some Variants of Concern, further work is needed to better understand how this variant behaves.