In a message sent to staff and students, the university confirmed there are at least 11 cases.
The Fife university said it expected numbers to rise, and that they were most likely a ‘new UK variant strain’ of the virus.
The message said: “I am sorry to report to you that we have this afternoon learned of a sudden and significant increase of covid infections amongst students currently in St Andrews.
"At this stage we have 11 confirmed cases affecting students living in four halls of residence, and private accommodation in town, and more than 40 are isolating.
"You will know that for many weeks, with your help, we have kept covid levels here very low, so this rapid increase in transmissions is especially concerning.
"Unfortunately we expect to see the number of confirmed cases rise over the next few days.
"It seems very likely this is the new UK variant strain of covid.”
NHS Fife Director of Public Health, Dona Milne, said: "We are aware of a sharp increase in COVID-19 infections linked to the University and we are working closely with our colleagues at the University of St Andrews and Fife Council’s Environmental Health Service.
"Over a number of months we have seen relatively low levels of COVID-19 within the University, and this is testament to the actions of the vast majority of the student population who appear to have adhered to the public health measures.
“It is clear, however, that in a small number of instances over recent weeks, the protocols in place have not been followed, particularly around gathering indoors, and it is very likely that the recent sudden increase in positive cases are a direct result of this.
“It is easy to think that as more and more people are vaccinated, and the number of COVID-19 cases reduces, that the virus is no longer a threat.
"COVID-19 remains highly infectious and even those who are otherwise well can become seriously ill.
“It is vital that even as the restrictions ease, we continue to follow the control measures in place if we are to suppress the virus.”