The charge relates to chants heard during the Sky Bet Championship clash between the sides at Oakwell on Saturday, November 9, which the Potters won 4-2, in the run-up to Remembrance Sunday.
Irish international McClean played for Sunderland AFC from 2011 to 2013.
An FA statement said: "Barnsley FC has been charged with a breach of FA Rule E20.
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"It is alleged that the club failed to ensure its spectators, and all persons purporting to be its supporters or followers, conducted themselves in an orderly fashion and refrained from using abusive and/or insulting words which included a reference, whether express or implied, to nationality and/or religion and/or beliefs, while attending an EFL Championship fixture against Stoke City FC on Saturday 9 November 2019.
"Barnsley FC has until Friday 10 January 2020 to respond."
In a statement on the club website, Barnsley said: “Barnsley Football Club has a zero tolerance policy on any form of discrimination. As a club, we are saddened to have had this charge brought against us. Since the incident was first reported, as a club, we have been thoroughly investigating and we will continue to do so.
“Anybody found to be involved in any form of abusive behaviour when representing Barnsley Football Club will be banned from attending matches.
“We will await and respect the outcome of the FA’s charge against us before communicating further on this matter.”
The news came just days after the FA launched an investigation into allegations of discriminatory chanting aimed at the 30-year-old Republic of Ireland international during the Potters' 5-2 win at Huddersfield on New Year's Day.
A tannoy announcement was made during the game at the John Smith's Stadium to warn spectators about the use of inappropriate language.
Derry-born McClean has been criticised by some in recent seasons for his decision not to wear a poppy on his shirt in the game closest to Remembrance Sunday, out of respect for those who died in the city on Bloody Sunday in 1972.
A statement from the Professional Footballers Association read: "James has been subjected to this type of vile abuse throughout his career, and he will be fully supported in the same way as any other individual who receives abuse based on their race, religion or nationality.
"It has become clear that this type of abuse is on the rise and is becoming a weekly occurrence for James. We will be talking with PGMO (Professional Game Match Officials) and the EFL to ensure that match officials are vigilant to this type of chanting and hope to see future action taken proactively on James' behalf."
Speaking on international duty in November last year about the regular abuse he receives, McClean revealed that he had been contacted by the FA before the trip to Barnsley and offered the association's support.
He said: "To give them their fair dues, I got contacted by a member of the FA on Friday before the Barnsley game just offering support.
"I wasn't expecting it, it was quite a shock, but in the same sense, credit where it's due. He didn't have to text me - he hasn't for the last eight years - but credit where it's due, he did to offer support, and they seem to be following up the chants from what happened on Saturday.
"Look, I've criticised them in the past, but I'm big enough as well to show and give credit where it's due."
Asked if he was tired of playing in England as a result of the hostility, the former Sunderland, Wigan and West Brom winger said: "No, not really. It doesn't bother me. It probably affects my wife and my ma more, but that's something I probably don't take into consideration, how they feel.
"For me, I just get on with it. I think over the years, I've developed a kind of thick skin and it's just water off a duck's back for me when it happens."