Arsenal looked to be heading for defeat after Seamus Coleman and Steven Naismith put Everton 2-0 up before half-time at Goodison Park, but Giroud scored a last minute equaliser following a strike by Aaron Ramsey, before picking up his injury.
Arsenal manager Arsene Wenger confirmed that Giroud would not be playing in the Champions Laegue game against Besiktas, but added that the length of his lay-off was as yet unknown.
However, respected French publication L'Equipe suggested there has been a bone break and the injury is much worse than first feared.
The report claims Giroud could be out until the end of November or the start of December.
Even while Giroud was fit, Arsenal were believed to be keen to bring in another striker but the French international's injury is only set to intensify their desire to make a move before the transfer window closes next Monday.
Giroud's injury would be a massive blow, no doubt about it, and it makes sense now for the Gunners to move for a striker; they will not want to rely too heavily on the inexperienced duo of Joel Campbell and Yaya Sanago.
They do also still have Alexis Sanchez and Lukas Podolski, while Theo Walcott could return next month too; but while those three can all play up front, none really fill you with confidence as main strikers and all look more comfortable playing alongside a stronger focal point.
Of the three players mentioned by L'Equipe, Remy would be the easiest deal to pull off as he has an £8.5m release clause. Arsenal's attitude towards the medical concerns that scuppered the French striker's move to Liverpool would likely be the only stumbling block if Wenger was keen on the player.
The Welbeck rumour has been doing the rounds for a few weeks, but it is believed that Manchester United do not want to sell the England forward to a direct rival for a top four place.
Meanwhile, any potential move for Cavani would be tough to pull off in one week, with a massive outlay probably needed to sign the Uruguayan.
A fourth option, not mentioned by L'Equipe, could be a late move for free agent Samuel Eto'o. The Cameroon international looks on the verge of a move to Everton, but could have his head turned by Arsenal. He proved to be a decent stand-in at Chelsea last season, and could provide a short-term fix for the Gunners until Giroud returns and/or better options emerge in January.
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