The City winger was felled by Watford's Jonathan Hogg on Monday and the result of the challenge has seen him sustain ankle ligament damage.
The injury is exepected to keep Conway out of action for three months.
Hogg was booked for the tackle but Malky Mackay was amazed that was all it warranted.
He said: "I thought it was a horrendous challenge and I didn't understand the decision of the referee."
Cardiff have four games left in which to secure a play off place.
Source: FOOTYMAD
