A large team of gardaí deployed to Fortunestown Road and Jobstown.
Both Centra and Lidl have confirmed incidents at their stores.
Lidl Ireland says they are aware of a 'very serious incident' at their Fortunestown Lane store in Dublin.
A digger was purposefully used to gain access to the Lidl premises by ripping into the roof and side wall.
Dramatic video footage of the incident has been uploaded online.
There are also reports from locals that the digger is being used in attempts to break open a safe taken from the store.
SHOCKING: The safe out of Lidl in Tallaght getting SMASHED— BenchWarmers (@BeWarmers) March 2, 2018
BREAKING: Lidl supermarket apparently looted in south County Dublin is now on fire and has been badly damaged by a JCB.— Michael O'Toole 🇮🇪🇪🇺 (@mickthehack) March 2, 2018
I am seething! Lidl in Jobstown, Tallaght after being looted and now has collapsed after being torn down? Is this the purge?! pic.twitter.com/Gwb6mEWkoE— john (@Scarlet4UrMa) March 2, 2018