Messi was reportedly targeted by a handful of disgruntled River supporters, with one person allegedly spitting at him while he made his way to passport control.
Barca team-mate Javier Mascherano and coach Luis Enrique intervened to diffuse the situation.
"I didn't see it, but I've been told about it," River coach Marcelo Gallardo told Argentine newspaper Ole.
"I want to condemn this behaviour, behaviour that is out of place. You need to be respectful. He's a player who was born in our country, is the best in the world and plays for our national team.
"Give him the respect he deserves. I don't agree with this behaviour at all."
River president D'Onofrio added on Fox Sports: "There's always some idiot, to put it mildly.
"I've just read that Messi had problems in the airport with some fan. Messi is the best player of Argentinian football, he's a gentleman... when he scored the goal, he raised his hands apologising.
"He congratulated the club for having got where we did, and he told me that when he was a youngster he was on the verge of becoming a River player.
"So I applaud him. You need to know how to lose and when to recognise the other team were better.''