The former Manchester United teammates were involved in a heated exchange in which Ibrahimovic appeared to tell the Belgian forward: "Go do your voodoo s***, you little donkey".
It was suggested Ibrahimovic was referring to comments made in 2018 by Everton majority shareholder Farhad Moshiri, who said Lukaku had declined a contract extension because a "voodoo message" told him to move to Chelsea - a transfer that never transpired.
Some accused Ibrahimovic of racially abusing Lukaku, with the Swede responding by stating on Twitter: "In ZLATAN's world there is no place for RACISM." United midfielder Paul Pogba also tweeted to say his old team-mate was "the last person I'd think of as racist".
Both players were booked following the incident before Ibrahimovic picked up a second caution for a foul in the second half of the game.
As part of the inquest, match referee Paolo Valeri has been summoned to explain his decision to book both players in the aftermath.
A statement read: "This morning, FIGC attorney Giuseppe Chine opened an inquiry into the verbal dispute between Zlatan Ibrahimovic and Romelu Lukaku in the Coppa Italia quarter-final between Inter and Milan on January 26.
"As part of this inquest, Chine has decided to summon referee Paolo Valeri, who will, in the next few hours, be called upon to give his statement regarding the sanctions that were handed out to both players during the game."
Lukaku had cancelled out Ibrahimovic's opener in the tie at San Siro before Christian Eriksen sealed Inter's progression to the semi-finals with a stoppage-time free-kick.