Shrewsbury Colleges Group said the case involved a part-time adult student at its London Road campus.
As a result five other students from the college have been contacted and told to self-isolate.
It is the latest education institution in the county to confirm positive Covid-19 cases – with Telford's Southall School, Charlton School, Hadley Learning Community and Captain Webb all reporting cases.
Around 80 pupils were also ordered to self isolate after a positive case at Llanfyllin High School in Mid Wales.
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In a statement the college said: "We have taken guidance from the dedicated service introduced by Public Health England (PHE) to support schools and colleges which is delivered by the NHS Business Services Authority, working to agreed PHE and Department for Education guidance.
"The student concerned is an adult part-time student studying one day a week at the London Road campus on the Access to HE course. The student is self-isolating in line with government guidance.
"We have identified the close contacts of the student through speaking to the student and their teachers and through using the lesson seating plans. The small number of students affected have been contacted and told to self-isolate in line with public guidance. The student with the confirmed case and their close contacts will only return to college after they have completed the required period of self-isolation and after being cleared to do so by the college’s Covid tracker."
James Staniforth, college principal, said: "Understandably, this news may worry students and parents in the local area. We take this very seriously, but the measures we have put in place to limit contact and to trace close contacts have enabled us to take action quickly and offer assurance to all students that the measures are effective. The use of seating plans and the room layout have limited the number of contacts as intended.
"The additional mitigations of the teacher zone, the application of the anti-viral barrier spray, the use of sanitiser, and the wearing of face coverings outside of the classroom continue to be critical in protecting staff and students. The application of the anti-viral barrier spray means that the two rooms affected are safe. Nevertheless, as an additional precaution they have been subject to both thorough cleaning this morning and to the reapplication of the long lasting anti-viral barrier spray.
"We have, therefore been able to limit the number of students needing to self-isolate following the case of Covid-19 at the London Road campus. Only students that have been contacted will need to self-isolate.
"The student did not have any interaction with students from the English Bridge and Welsh Bridge campuses and had very limited contact with students at London Road campus.
"The college remains open and students should continue to attend if they are well."