Garcia, who was diagnosed with leukaemia in February 2015, was surrounded by his wife and family.
The club have confirmed a minute’s silence will be observed before Saturday’s League One home game against Peterborough.
“This is such tragic news, and we send our deepest condolences as a club to Juan Carlos’ family and friends, who have had to sit by and watch this sad story unfold over the past few years,” said Latics chairman David Sharpe.
“We have offered what support we can but, despite the best possible treatment at Christie’s Hospital, Juan Carlos has tragically not been able to beat this terrible illness.
“At just 29 years old, he was far too young to be taken and our thoughts are with his family at this sad time.”
Garcia joined Latics in the summer of 2013 from Honduran club Olimpia, but made only one appearance - a League Cup tie at Manchester City - in September of that year.
He went on loan to Spanish side Tenerife the following summer, but returned to England midway through the 2014/15 season, when he was first diagnosed with the illness.
Following the end of his Latics contract in 2016, Garcia was granted permission to remain in the UK to continue his treatment, before moving back to his home country towards the end of 2017.
He represented Honduras at the 2014 World Cup finals in Brazil.
Chris McCann was one of a number of former colleagues quick to voice their upset on social media.
“Very sad to hear about the passing of ex team mate Juan Carlos Garcia at just 29 years of age,” tweeted McCann, now playing in America with Atlanta United.
“Had the pleasure of getting to know him very humble down to earth person. Thoughts with his family and friends at this tragic time.”
Current captain Sam Morsy posted: “Really sad news about a former player RIP Juan Carlos prayers are with him and his family.”
Max Power added: “Terrible news. Rest in Peace, Juan, taken so young! Prayers with his family.”
Latics legnd Mike Pollitt, now goalkeeper coach at Rotherham, tweeted: “Thoughts go out to the family of Juan Carlos Garcia, my former team-mate at Wigan. Terrible news at such a young age. RIP my friend.”
PFA chief executive Gordon Taylor posted: “Having got to know Juan Carlos well since his diagnosis, and helped him and his family during his treatment, his love for life and human qualities shone through. He will be sadly missed by all who knew him. May God bless him.”
And Latics player liaison Karen Armstrong, who perhaps knew the player and his family more than anyone, shared a touching tribute on Instagram.
“Last night I lost my beautiful friend,” she wrote. “Three years of a horrible battle and so much pain and suffering, but he remained so strong and an absolute gentleman until the end.
“Juan Carlos I am so glad I got to have you in my life. I am so grateful I will have your wife and kids as a part of me always.
“I’m so honoured that you were my friend. I’m going to miss you every day. Can’t believe I will never hear your voice or see your lovely face again. Sleep well my my love until we meet again.”