Championship team Wigan announced last week that the 26-year-old, who has 34 international caps, was admitted to hospital after developing a blood disorder.
"He has a form of leukaemia. Juan Carlos is in the Christie Hospital in Manchester," Mackay told reporters.
"It's something that is obviously a real blow for Juan Carlos's family and everybody connected with the football club. We're going to make sure he gets the best care possible.
"I went to see Juan Carlos and he was incredibly upbeat and his spirits were strong. Everybody at the club is wishing him all the best as I'm sure all our fans are," said Mackay.
Garcia, who joined Wigan on a free transfer in 2013 but has made just one appearance for the club, recently returned from a loan spell with Tenerife in Spain.
