The Sweden international moved to the Gunners on loan from Spartak Moscow for the remainder of the campaign.
However, reports soon surfaced that the 31-year-old would be set for a spell on the sidelines after sustaining an injury in the days prior to sealing his move to North London.
Although Wenger concedes to have known that Kallstrom would not be ready for first-team duties immediately, the Frenchman says that his hand was forced due to how late in the transfer window it was.
"He arrived here and fell on his back two days before. First of all it's very difficult to identify a player who can come in of that stature on a free loan," he told Sky Sports following his side's 2-0 win over Crystal Palace.
"We made a medical of his back and found out he had a little microfracture. We have all played with microfractures.
"Then Spartak Moscow accepted to share the costs. As long as he's injured, they pay. But I had a decision to make. I take nobody or Kallstrom, on Friday after 5 o'clock."