Barnes put in a full-blooded tackle on the Blues midfielder during Saturday's 1-1 draw at Stamford Bridge, leaving his foot up and studs showing as he made contact with Matic's leg.
Having initially gone to ground in pain, the Serbian ran towards Barnes and bundled him to the ground, earning a red card from referee Martin Atkinson.
Chelsea are reportedly set to appeal against Matic's three-game ban, but manager Jose Mourinho had also suggested that action should be taken against Barnes, who was not even cautioned.
But the FA revealed on Twitter that it would not be punishing the Clarets forward, and explained the rationale over five posts.
They read: "In the vast majority of challenges for the ball, no retrospective action is taken as the incident has been seen by the match officials.
"Retrospective action introduced as deterrent for 'off the ball incidents' [e.g
kicks, stamps etc.] committed out of sight of officials.
"Whole game in agreement that, in vast majority of cases, match officials are best-placed to deal with incidents to avoid re-refereeing.
"In line with this rationale, FA confirm no further action in relation to Ashley Barnes as incident was seen by the officials."
The FA verdict is unlikely to find favour with Mourinho, who betrayed a tangible sense of injustice during a television appearance at the weekend.
The Portuguese, who was fined £25,000 earlier this season for claiming there was a media 'campaign' against his side, told Sky's Goals on Sunday programme that Barnes' tackle was at least as bad as one that earned his striker Diego Costa a three-game ban last month.
"I would like to know how to you, Sky Sports, describe the actions of the Burnley player yesterday? My English is not good enough to find a word," said Mourinho
''When you think 'Diego crimes' after he puts his boot on a hand, when this is 'Diego crimes', the minimum you have to say is 'criminal tackle' (by Barnes)
''When Diego Costa has a three-match ban, probably three matches to Matic..
tell me how many matches this player deserves?''
Source : PA
Source: PA