The teacher - who works for Amethyst Sixth, which is based at Aldersley High School, in Wolverhampton - is now self-isolating after the positive case was confirmed on Monday.
Five other members of staff are also awaiting test results.
Students in Year 12 and 13 have been told to self-isolate for 14 days following guidance from Public Health England.
They are being taught virtually ahead of a planned return on September 21.
The sixth form building is based on a separate part of the school which has remained open to secondary students.
Amethyst Sixth also caters for past students of Moreton School, based on Old Fallings Lane, Wolverhampton - which is run by the Amethyst Academies Trust. The trust also runs Aldersley High School.
Parents and carers were informed of the coronavirus case in a letter issued yesterday.
The school's executive principal, Nicola Davies, told the Express & Star: "We have a joint sixth form for both schools Aldersley High School and Moreton School called the Amethyst Sixth form and the building is separately housed on the Aldersley High School site. There are 250 students overall.
"On Monday, a sixth form teacher tested positive for Covid-19 and we are awaiting results for a further five members of the sixth form teaching team.
"We are confident that all procedures have been followed and that sixth form students are not at risk however working with Public Health England and as a precautionary measure we have asked sixth form students to self-isolate for 14 days.
"All of our students are allocated laptops when they join Amethyst Sixth and this has enabled them to immediately access live teaching so that they are able to interact with their teachers.
"Mrs Gavin, our senior assistant headteacher with responsibility for our sixth form, is delighted that 100 per cent of students are attending live lessons today.
"We look forward to welcoming students back into the building on September 21."