The incident happened in Ballyliffin on Sunday night.
The marked Garda car struck two young men at Annagh Crossroads on the R238 at round 10.30pm.
The details surrounding the incident are still unclear.
One of the young men was rushed to Letterkenny General Hospital but his injuries are not understood to be life-threatening.
Garda forensic officers remained at the scene all day on Monday as a full investigation was launched into the circumstances surrounding the incident.
A Garda spokesperson would not comment on the matter as it had been passed to the Police Ombudsman for further investigation.