Rodriguez was seen pinching his nose and saying something to Brighton defender Gaetan Bong, who is black, after an on-field confrontation during the January 13 game at The Hawthorns.
Bong, a Cameroon global, was subsequently interviewed by FA officials at Brighton's training ground while Rodriguez had a hearing at Wembley.
Cameroonian defender Bong posted a since-deleted comment on his own Twitter feed after the game, saying: "Some words should not be said on a football field and specially not by players Rodriguez words are unforgivable for the man I am!"
"Jay Rodriguez has been charged following an incident during the West Bromwich Albion versus Brighton and Hove Albion match on 13 January 2018", the FA said in a statement. "It's a situation which is not ideal for Jay". It's not just about us losing Jay for five games, it's a bit more serious than that, his future after the game - whether he wants to be a coach or go into business.
The Latest Update On The Injuries To Robbie Henshaw & Tadhg Furlong
And when captain Rory Best went over for Ireland's sixth try, the visitors were facing a humiliating defeat. Get your weekend sorted with our guide to live streaming the Ireland vs Italy Six Nations 2018 match.
"Jay is upset about it, he has a good mental capacity to deal with things and hopefully..."
Both players have made their cases at respective hearings since the game before, on Thursday, Rodriguez was officially charged but his club remain fully behind the forward. We are in that kind of world at the moment where everybody has to be so careful and even now talking about it I am nervous - everybody is.
"I spoke to the PFA [Professional Footballers' Association] this morning, I tried to contact Kick It Out this morning, but I have had no reply. It's an accusation he denies and we're going to support him", Pardew said.
Rodriguez, 28, who won one England cap in 2013, has until February 16 to respond to the FA charge.