The Frenchman has endured something of a nightmare start to the new campaign this term, and Wenger preferred Theo Walcott to the Les Bleus international for their last Premier League game against Stoke City.
Walcott rewarded Arsene Wenger's faith with the opening goal, and while Giroud netted a second-half header, the forward's celebrations were strangely subdued given what had previously been a poor week.
Giroud was booed by his own fans earlier that week after missing a hatful of chances for France as they edged out Serbia 2-1, and although his national side were victorious, it was an evening to forget for the ex-Montpellier man.
After being dropped to the bench for the visit from Stoke, Giroud was handed a chance to stake a claim for an inclusion against Chelsea this weekend, but the 28-year-old let himself down with a red card as the Gunners slipped to a 2-1 reverse against Dinamo Zagreb in the Champions League on Wednesday.
To make matters worse for Giroud, he could only watch on from the stands as Walcott grabbed a late consolation for Wenger's men, and former Manchester United defender Rio Ferdinand felt that the England international should have been included from the start ahead of his teammate.
"They've got to give Theo a chance [up front]. He's been there all these years, he's mooted about wanting to be a centre forward," Ferdinand told BT Sport.
"I think Wenger is hurting Arsenal by not giving him a sustained period playing up front. Give him a chance to prove himself, if he can't do it then go out and buy someone."
Giroud scored an impressive volley against Crystal Palace last month, but the strike was a stark contrast to how he has generally been performing for his side so far this term.
The target man offers a very different threat to that of the pacey Walcott, and Giroud's touch and strength are valuable assets for Arsenal, and while two goals in five appearances is not a poor return, the feeling persists among many that the striker is a level short of what is required for a team that has pretensions of winning the Premier League.
Speaking after Giroud's disappointing outing with France last week, Wenger maintained that his centre-forward retains his "full support".
Wenger told Arsenal's official website: "There is no striker in the world who has not been questioned. When he missed a chance and is booed, that can happen. He has my full support and I believe that is part of being a striker."
Supportive Wenger may be, but Giroud may now be forced to endure a spell as second choice striker at the Emirates, despite the manager's refusal to sign a goalscorer in the summer transfer window.