The Argentinian was taken off after 27 minutes at Ewood Park, but his withdrawl counted for little as City romped home 4-0.
"It's too early at the moment," said Platt. "It's a groin injury and the early indications are that it is not as bad as we first thought.
"Having said that, if we had a game in the week or next week, he wouldn't play. With the international break, who knows? It depends how quickly he heals up. It's probably touch and go for Aston Villa, but we will look at it in the next 48 hours.
"I would think at least two weeks, but I'm no medic."
The win has kept City second on goal difference in the Premier League table, behind rivals Manchester United.