The Northern Ireland international had gone over to applaud the visiting supporters following their 3-1 FA Cup fifth-round defeat, but went down clutching his face as he approached the away end.
Brunt, who suffered a cut under his left eye, said a coin had been thrown at him by the fans, while boss Tony Pulis claimed the player could have been blinded.
The FA will look into the incident, as well as the crowd disturbances in the Baggies' end of the Madejski Stadium.
A statement from the organisation on Saturday evening read: "The FA is investigating the incident in which an object was thrown from the crowd at Chris Brunt at the end of the Reading v West Bromwich Albion game on Saturday (20 February 2016) as well as the crowd disturbances in the away section of the stadium.
"We strongly condemn any such behaviour and will work with both clubs and the authorities to identify those responsible."
A Thames Valley Police spokesperson said: "The incident will be dealt with as an assault and we will be working with West Bromwich Albion and Reading to resolve the issue and identify anyone involved."
The midlands club later released a statement vowing to impose "the severest of sanctions" on the culprit.
"All our true supporters will join the club in condemning the sickening behaviour of a few individuals at the end of our FA Cup fifth-round tie at Reading," it read.
"They will be horrified at the sight of one of our longest-serving players, Chris Brunt, being struck beneath an eye by a coin as he attempted to show the team's appreciation to the travelling fans for their backing during an ultimately disappointing afternoon.
"The incident should not be allowed to blacken the good name of West Bromwich Albion and its loyal supporters.
"We are working with all the relevant authorities to identify as quickly as possible the offender, who can expect the severest of sanctions by the club for his actions.
"We are now sure all our supporters will be anxious to show the true spirit of the genuine West Bromwich Albion fans for the forthcoming fixtures, beginning against Crystal Palace at The Hawthorns on Saturday."
Press Association Sport understands the fan who allegedly threw the coin has been identified by stewards in a picture which has now been passed to police and West Brom will issue a lifetime ban if they are found guilty.
Brunt did hand his shirt over to a supporter after gesturing and remonstrating with another group who had made their way to the front of the stand as he moved closer to apologise for Albion's exit.
"I've still got the 50p," the 31-year-old said. "I spotted a little girl in the front row and wanted to give her my shirt.
"Obviously there's some people in the front who were angry, understandably, because we didn't play well or get the result we wanted.
"But there's absolutely no excuse for that and no place for it in football. I've been here a long time. Obviously we all get our fair share of stick, but to be hit with a coin by your own fans is absolutely disgusting.
"The guy who threw it knows who he is and knows all this week where I'll be, and next Saturday if he wants to come and have a word about it that's not a problem - I'll meet him wherever he wants.
"I've been here a long time and I've loved my time here and that's the first time I've been ashamed of our supporters. A small minority obviously ruined it for the rest of the 4,000 who were there and paid good money for a day trip."
Pulis said: "We have seen an incident where a lad who has played over 300 games for this club could have had his eye out.
"He has a cut and it's not too far away from his eye - it's an inch away from striking him in his eye and if that happens we're talking (about) a very, very serious problem.
"It's barbaric. That's not acceptable. West Bromwich Albion is a fantastic football club, a famous club, but you can't condone that.
"I think the police have to get involved in this. I don't think you can allow that to go by. That's criminal, and I mean criminal.
"This has got to be one of the worst things I have seen, for Chris to have a coin thrown at him from his own supporters having been at the club for such a long time. Every decent supporter of the club will be absolutely devastated it has happened to their football club.
"It's the way the game is going. Social media and everything else builds up an anti-feeling if things are not going well at football clubs. We have to be very careful with it."
Albion goalkeeper Ben Foster took to Twitter to label the coin-thrower a "disgrace".
He posted: "Whoever threw that coin at Chris Brunt today, thousands if not millions of kids will see or hear about it. You're a disgrace."
Reading boss Brian McDermott added: "It's outrageous, stuff like that, it's not right and proper. We will co-operate with whatever we have to and make sure we find the person who threw it."
Goals from Paul McShane, Michael Hector and Lucas Piazon sent Reading through to the FA Cup quarter-finals for just the fifth time in their history. Darren Fletcher's opener for West Brom was eventually worthless.