The FA's action comes in relation to an incident at half-time during Sunday's Premier League match at the DW Stadium.
Carver was incensed with Wigan forward Callum McManaman following his challenge on Massadio Haidara as the players left the field and Barrow also became embroiled in the fracas.
Both men were sent to the stands for the second half of the match, which Wigan went on to win 2-1 courtesy of Arouna Kone's last-minute goal.
Haidara was carried off with a knee injury and is still waiting to discover the full extent of the damage.
The fall-out from the incident has led to a war of words between the two clubs, although the FA ruled earlier on Tuesday that McManaman would face no retrospective action.
Both men have until 4pm on Friday, 22 March, to respond to the FA charge.
How pathetic is this!! The FA can charge people for arguing but do not give any punishment to the reckless tackle that caused the problem! One of the official's saw the challenge but decided it was not a career threatening assault! The FA and the official's concerned are a joke, I honestly don't believe Mc Mannaman meant to cause injury, but it was definitely reckless, and after the fuss of Nani and the outcry of how 'dangerous' his challenge was, can any sane person say it was anywhere near likely to cause the damage this challenge may well do, it is quite telling that even now 2 days later that a medical assessment can still not define how bad the injury is- toonman