Eastleigh College said that staff were made aware on Monday of two confirmed cases.
The two affected students are now self-isolating and the college has identified and made contact with everyone who was in close proximity to them.
Hampshire Protection Team has been working with the college and have confirmed that the last date of isolation for the learners is October 24.
The college, which has says it has been able to confirm that the cases are not connected in any way.
A spokesperson for the college said: “Through our seating and group plans we have been able to quickly identify the learners who were in proximity to the two affected learners.
“On Tuesday 20 October the College made contact with each individual identified, and also made contact with the parents, guardians or carers of these individuals where they are under 18, or under 25 and have an Education Health and Care Plan.”