Jenas joined the Villains in the summer on a season-long loan, but only made his debut last month against Norwich City.
However, the 28-year-old ruptured his Achilles tendon on his first start for the club during the 1-0 defeat to Manchester United.
The midfielder will now return to parent club Tottenham Hotspur for treatment but, due to Premier League regulations, Villa will have to pay his wages for the rest of the campaign.
"I think you do an agreement with a club and you take that on as far as the agreement goes," McLeish said.
"The club which takes him on loan has to fulfil that agreement. Jermaine will go back to Tottenham but we've still got an agreement with Tottenham.
"We can only sign one more loan player in January now because Jermaine still counts. We've got to look at that rule."
It has been reported that chairman Randy Lerner will be forced to pay out £1.3 million, including medical bills, for Jenas, who played only 108 minutes of football for the Premier League side.
Nevertheless, McLeish has already targeted January as the chance to bring in a replacement for the midfielder, with the Premier League unlikely to relax their rules regarding loan players.
"We've lost a player and that is it. We have to get on with it and we'll see what we can do in January," the Scot added.
"If there are going to be additions then we need to trade carefully.
"I spoke to Randy Lerner briefly and also to [chief executive] Paul Faulkner so the stance is the same in the summer.
"We have to trade before we can bring new faces in, but that's not to say we definitely won't do something if no-one goes out the door, so there are still possibilities."
