The club described it as "a personal choice" and the shirt is now subject of a bidding war as the winger agreed before the game to give it away.
St Patrick's Athletic defender Ger O'Brien, a former Derry City team-mate of McClean's, asked for the shirt in order to raise money for Crumlin Children's Hospital in Dublin.
He told TheScore.ie: "I knew he was coming over for the [PFA of Ireland) awards so I gave him a bell a week or 10 days ago to ask him to bring over a shirt.
"I wanted to auction it for charity. I didn’t know until he got here about all the hype surrounding what had gone on on the day."
McClean attracted negative publicity for his decision not to wear a poppy, but it looks like good news for the hospital, as O'Brien explained.
"I only put it up at six or seven o'clock yesterday evening and I got to €400 (£320), but there’s plenty of private messages and things like that. RTE and a couple of other stations and radio shows contacted me so I put the deadline to next Monday now and I’m hoping to get a fair few quid for it."
O'Brien said McClean, who was born in Northern Ireland but represents the Republic of Ireland, did not deserve to be criticised.
"It’s own personal choice, whether people think he’s right or he’s wrong, people should respect his decision," he said.
"He has his own reasons for doing it - probably he’s going to get plenty of criticism in the UK and he’ll get plenty of pats on the back in Ireland. That’s just the way the politics works in this world and the history of everything."
For more information on the auction follow Ger O'Brien @gerramia on Twitter.