The Sky Bet Championship club announced last week that the 26-year-old Honduras international had developed a blood disorder and was in hospital for treatment.
Signed by Latics in 2013, Garcia recently returned from a loan spell with Tenerife in Spain.
Mackay said: "We've had some bad news as far as that's concerned - he has a form of leukaemia
"Juan Carlos is in the Christie Hospital in Manchester
"The club doctor, Doctor (Ansar) Zaman, has been truly sensational as far as the care and attention with the whole dealing of the matter as far as Juan Carlos feeling ill and having problems - from that point to the point where we got him to a specialist quickly and got the diagnosis done
"(Chief executive) Jonathan Jackson, myself and the doctor have had various chats on it
We've flown his mother, his wife and his sister over form Honduras to be with him and arranged accommodation close to the hospital as well.
"It's something that is obviously a real blow for Juan Carlos' family and everybody connected with the football club
We're going to make sure that he gets the best care possible
"I went in to see Juan Carlos and he was incredibly upbeat and his spirits were strong
He's going to fight this and make sure he gets through this for the sake of his wife and kids
Everybody at the club is wishing him all the best as I'm sure that all our fans are."
Source : PA
Source: PA