The leaves of absence were taken by workers at Glasgow City Council during the 17 days between the opening ceremony on July 27 and the close of the Games on August 12.
The figure is over 400 days more than the same period last year, when staff took 3818 sick days.
The sick days were taken by staff among the 19,252 workers directly employed by the council such as teachers, office staff, press officers and executives.
Jonathan Isaby, of TaxpayerScotland, said: "It's simply not fair that taxpayers keep having to pick up the bill for excessive sick leave at their local council.
"If there is any evidence that any of those who took sick days during the Olympics were not genuinely sick, the council must crack down hard on such behaviour and make an example of any staff who skipped work."
The figures were revealed through the Freedom of Information Act.
The worst offenders were in the Social Work Services department, whose 4345 staff took 2311 days. The same department last year took 1944 sick days, nearly 300 fewer.
A spokesman for Glasgow City Council said: "Our sickness absence rates have been coming down and we've saved more than £17 million over the last few years as a result of robust measures we've implemented."