Arsenal have only added young French striker Yaya Sanogo to their squad this close-season, with the club missing out on players such as Luiz Gustavo and Gonzalo Higuain.
And Giroud believes they need reinforcements, particularly up front, if they are to compete.
"In my opinion, it's necessary for the club to recruit another striker," he told Le Parisien.
"Obviously, I think about it a little bit. It may change the play one day, especially if it’s a high-profile signing.
"It's useless lamenting this, though. I know what I have to do and what I'm capable of. I’m focusing on me and my work. The coach is counting on me, so I don't think too much."
Arsenal lost 3-1 to Aston Villa on Saturday in their Premier League opener, with fans calling for Wenger to spend money on new players.
The club are reported to have seen a bid for Newcastle United midfielder Yohan Cabaye rejected on Monday.
Giroud is expected to lead the line for Arsenal on Wednesday as they take on Fenerbahce in the UEFA Champions League play-offs.
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