The key reason is the absence of centre-back Kolo Toure for around a month while he plays in the African Nations Cup with Ivory Coast.
"He will be a loss, for sure. It is disappointing that he is not going to be with us for much longer."
Djourou has started 12 of Birmingham's 17 Premier League games to date and has impressed at times.
"You have to respect Arsenal's decision," McLeish added.
"Johan is a big presence of a boy, no doubt about that, and those kind of players seem to be a feature of many a squad in the Premier League."