Barco, who did not play in the game, came on to the pitch at full-time and was hugging team-mates near Bellingham when the England midfielder walked over and slapped him.
It sparked a small melee as players from both sides got involved before Bellingham walked away.
It is not known what prompted the reaction, but footage showed Barco running on the pitch after Enzo Fernandez’s 85th-minute equaliser and celebrating in front of the England players.
Former England goalkeeper Paul Robinson, commentating on the match for BBC Radio 5 Live, described Barco’s actions as “probably the worst example of sportsmanship we’ve seen at this World Cup”.
Bellingham could face action from Fifa’s disciplinary committee for violent conduct.
Being found guilty of such a charge would result in the 23-year-old being suspended for Saturday’s bronze medal match against France in Miami (kick-off 22:00 BST).
However, Fifa is more likely to consider the act as petulant rather than violent.
The laws of the game state there is no red-card offence if a player deliberately strikes an opponent on the head and the force used is negligible.
Lautaro Martinez headed the winner for Argentina in the second minute of stoppage time, ending the hopes of an England side who had taken an early second-half lead through Anthony Gordon’s goal.
Barco, 21, who plays for French side Strasbourg and previously had a spell at Brighton, is expected to join Chelsea.
He has featured once at the tournament as a second-half substitute in a 3-1 group win against Jordan.
The first half of Wednesday’s match in Atlanta was feisty with 19 fouls, as American referee Ismail Elfath struggled to keep control.
Bellingham, who has scored six goals in the tournament, also had a confrontation with Argentina captain Lionel Messi in the fourth minute after England midfielder Elliot Anderson had been fouled.
“We were really just discussing a foul, actually,” Bellingham is reported to have said. after the match.
“It wasn’t anything bad. I’m sure everyone will do their thing and make it a big deal, but it was nothing.”
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