The Parkhead side have already lost Dedryck Boyata for the next three months after he ruptured knee ligaments in last week’s warm-up clash with Slavia Prague.
And there are now fears skipper Brown could also miss Friday’s qualifier with Linfield in Belfast after lasting barely half an hour at the Tallaght Stadium.
The Scotland midfielder was replaced by Nir Bitton after 32 minutes and trudged down the tunnel at half-time with his knee heavily strapped, leaving Brendan Rodgers to pray his influential captain has not suffered lasting damage.
That injury worry aside, Celtic were utterly untroubled as they swatted the Dubliners aside.
Mikael Lustig fired them ahead with a composed finished before Stuart Armstrong doubled the Parkhead side’s advantage.
Moussa Dembele - making his first appearance since injuring his hamstring in the William Hill Scottish Cup semi-final - and Scott Sinclair then got themselves on the scoresheet before the break.
Second-half goals from James Forrest, Sinclair, Armstrong, Jonny Hayes and Tom Rogic completed a resounding win.