Officers have not revealed how many arrests have taken place or who they are, but stressed that their investigation into Adam Smith College, in Fife, was continuing.
Detective Chief Inspector Gordon Crossan, who is overseeing the inquiry, said: "I can confirm that a number of people have been arrested so far as part of the inquiry into allegations of fraud at the former Adam Smith College.
"Further details will be available when a report is submitted to the procurator fiscal."
Police began carrying out inquiries into the running of Adam Smith College, in Kirkcaldy, which is now part of Fife College, after two separate inquiries by auditors KPMG and the Scottish Government, which resulted in the institution being ordered to pay back £5.5 million in EU grants.
The investigations uncovered voluntary severance payments made to two individuals that were not in line with college policy, as well as a lack of documentation around a number of decisions, including the personal use of college facilities and suppliers.
According to a report by accountancy firm Grant Thornton, which was made public last year, KPMG found the college's financial regulations had not been adhered to when it came to hiring two companies for a marketing strategy review.
KPMG also found evidence the college had submitted claims to grant funding bodies that were "inaccurate, unsupported by evidence and overstated" since at least 2007.
A later investigation by Scottish Government auditors found "significant irregularities", including the apparent systemic over-claiming of staff time, according to the report.
The inquiry into the college's finances began after an investigation by the Scottish Funding Council (SFC) into bullying at the institution was carried out in 2012.
Former principal Dr Craig Thomson resigned in March 2012, a week after he had been suspended indefinitely when the SFC launched its investigation into allegations of bullying, intimidation and the misuse of funds.
His replacement, Ian Harring-ton, was suspended as interim principal on the orders of the college board while the investigations into the misuse of funds were carried out. He later left the college.
Last year's Grant Thornton report stated: "The [Scottish Government] auditors found significant irregularities, including the apparent systemic overclaiming of staff time.
"The Scottish Government has subsequently required the college to repay the full value of EU grants received."
The report went on to say that the college's financial position had been "significantly affected" by the requirement to repay the European grants.
Adam Smith merged with Carnegie College in Dunfermline to form Fife College in August last year as part of a Scotland-wide reorganisation of the further education sector.
A spokeswoman for the new college would not comment while the police investigation was ongoing.