The flags, which numbered in the hundreds, were deemed to be "provocative messages of an offensive nature," UEFA said in a statement.
Fans, who had been warned by the Scottish club not to display flags before the Oct. 25 game, could be heard singing "You'll Never Walk Alone" while holding the Palestinian flags in a video shared widely on Instagram.
Supporters also unfurled two large banners at Celtic Park that read "Free Palestine" and "Victory to the Resistance."
The war erupted in early October, when several thousand Hamas militants broke through Israel's formidable defenses and poured into the south, killing at least 1,200 people, mostly civilians, and taking scores more captive.
Israel responded with weeks of devastating airstrikes on Gaza, followed by a ground invasion. More than 11,000 Palestinians have been killed during the Israeli offensive, according to the Health Ministry in the Hamas-run territory. It does not differentiate between civilians and militants, though some two-thirds of the dead have been identified as women and minors.
Celtic are fourth in UEFA Champions League Group E on one point after four games.
They were also fined £10,000 for fans blocking passageways and using pyrotechnics.
Information from The Associated Press was used in this report.