Birmingham's record signing Benitez, signed from Mexican side Santos Laguna for £7.75million, has finally linked up with his new team-mates after being granted a visa.
He upset McLeish by playing in a charity match before arriving in Birmingham at the weekend and is still recovering from a shoulder operation in May and is unable to join in fully with training.
McLeish told the Birmingham Mail: "Christian is still at a stage where he's not going to make any contact training at the moment. It will be more of the running variety.
"We've done the tests on him and he's a a bit behind on the fitness as well.
"These situations happens when you buy players when they come from South America. They have finished their season late and they need a little more rest. You've got to be fair to them.
"The important thing is having these guys for the whole season, not just one game, and that's what we will be working towards."
McLeish admitted: "For players to get fully fit, ideally a month is about it. We're guided by the sports science and fitness department and they will recommend a month for players to get top fit, top sharp.
"Christian had a 12-week recommendation from getting his shoulder pinned from specialists that he could not be involved in any contact, and we have to respect them.
"I know he participated in a charity game and we were fortunate he didn't get an injury because that was inside the timeframe for his rehabbing.
"He's got away with that and we need to see what level he is at during the coming days training."