It happened about 23:00 local time, during Ramadan nightfall prayers at the Masjid Maryam mosque, in Ballybrit.
Irish national broadcaster RTÉ is reporting the mosque's Imam Ibrahim Noonan believes it was a targeted incident after Saturday night's terrorist attack in London.
He said he initially thought the huge bang was caused by an electrical fault.
It is understood CCTV footage shows suspects fleeing the scene after shattering a window.
Garda (Irish police) confirmed they are investigating the criminal damage at the premises in Ballybrit, County Galway.
They are appealing for witnesses and reviewing the CCTV. No arrests have yet been made.
A mosque in Galway was vandalised on Monday night while a full congregation of worshippers was inside.