The news has forced the college to temporarily close the Science, Technology, Engineering and Maths Centre, and the automotive technologies campuses.
Yiannis Koursis, principal and chief executive of Barnsley College said: “We sought advice from Public Health England immediately and took all appropriate actions.
“I want to reassure all students, parents and staff that our college campuses continue to meet the Covid-secure measures and remain open.
“Anyone who has symptoms should not attend college and should be tested as soon as possible.
“Thank you to everyone for their continued support in keeping our college community safe.”