Ferguson suffered the setback in a first-half challenge from Gunners midfielder Samir Nasri.
But the former Scotland international stayed on the pitch to help Blues gain a shock 2-1 win although he is rated doubtful for this Saturday's home Barclays Premier League clash with West Brom.
"Barry Ferguson played an hour with a broken rib at Wembley," said McLeish.
"It shows that his pain threshold is frightening and also the character of the guy to do that. We all know how painful a broken rib can be.
"I think it happened in a challenge with Nasri. He has taken a right bash in the ribs.
"It has been confirmed that there is a stress fracture and he is a doubt for the weekend."
Source: PA
Source: PA