Hamilton and Mercedes team principal Toto Wolff skipped the event on Thursday (16 December) after being controversially pipped to the championship by Max Verstappen.
Mohammed Ben Sulayem, the newly-elected president of the Fédération Internationale de l'Automobile (FIA), said: "First of all, as a driver, I would feel emotional but at the end of the day rules are rules. So we are going to look into the side where the technical rules are there to be employed.
"Was he in breach? I have to look into it. We have to be following our rules, but in the meanwhile it doesn't stop us from making a champion feel good about the sport.
"It's easy to be nice to people, it's cheap to be nice, and also to motivate people."
He added: "If there is any breach, there is no forgiveness in this."
Article 6.6 of the F1 regulations states that the top three drivers in the championship must be present at the gala, though it is unclear what type of sanctions are at the FIA’s disposal.
Red Bull's Verstappen stormed past title rival Hamilton on the last lap of the season-ending race at the Yas Marina Circuit at the Abu Dhabi Grand Prix last Sunday (12 December), having benefited from a late safety car that bunched up the pack.
Hamilton appeared to be charging to glory, easily holding Verstappen at bay in the closing laps, only for a crash for Williams' driver Nicholas Latifi to change the course of events.
Confusion reigned as race director Michael Masi changed his mind to allow lapped cars to pass the safety car – meaning Verstappen had a clear run at Hamilton in the final lap and, on much faster tyres, made his move to claim a first F1 title.
Commenting on the controversy, Ben Sulayem said: "I have promised we will look into the rules and make sure that any situation of this sort that occurs in the future, we will have an instant solution for it.
"We had a meeting with the drivers and I feel that what happened has been declared now. The FIA took a decision, we discussed it and there was a statement, and now we have to start the new season.
"We have to be proactive and reactive. I feel it is a time where as a driver I would be so upset for a while, but time is a factor that will cool. After the holidays and Christmas, in the new year we will start afresh."
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