"We have sent him for an X-ray and we hope he has not broken his ankle," said Mackay.
"I thought it was an appalling and horrendous challenge. It was a scissors tackle. I can't understand the referee's decision on it. It was a sending-off for me.
"I'm disappointed for Craig because he started the game really well. He was having a good go at Carl Dickinson and was looking good."
Conway has played 37 times in all competitions for Cardiff since joining from Dundee United last summer.