The unnamed Vision West Nottinghamshire College tutor was sending a private email which was "inadvertently" displayed on a smartboard for his whole class to see.
The college said the tutor has since been suspended while it investigates the incident.
One student who asked to remain anonymous said: "I am absolutely shocked that a professional could do such a thing, especially during a lesson.
Another student said: "It actually made me feel sick."
The tutor's students have since made 'memes' about the incident.
Andrew Cropley, college principal and chief executive, said: “I can confirm an incident took place in a class whereby a private email from a tutor, containing explicit content intended for another adult, believed to be his partner, was inadvertently displayed on a smartboard and seen by students.
“The college acted swiftly by immediately suspending the tutor, pending the outcome of an investigation.
“Clearly, this was wholly inappropriate conduct that fell significantly below the high professional standards expected of all our staff.
“I have written to the students and their parents and guardians to offer my sincerest and unreserved apologies.
“However, although deeply regrettable, it is important to stress this was an isolated incident that in no way reflects the behaviour, conduct and care exercised by our teaching staff day in, day out.”