Hamilton was an opening corner retirement after turning across the front of team-mate George Russell.
Officials investigated the incident post-race and fined Hamilton €50,000 – just over $80,000 – with half suspended.
“The FIA notes that Lewis was apologetic during the subsequent stewards hearing in to the incident and acknowledged that the crossing was a serious safety breach.
“However, in view of his role model status, the FIA is concerned about the impression his actions may have created on younger drivers.”
The punishments open to officials are outlined by the FIA International Sporting Code and the F1 Sporting Regulations.
The latter primarily relates to grid penalties should enough reprimands be handed out within the same championship (five) and otherwise defers punishment to that laid out in the Sporting Code.
There, penalties range from a warning to fines and sporting penalties including time being added to a race result.
At the more serious end, those sanctions also include disqualification, suspension, and exclusion.
It's understood the FIA is mindful of the comparative lightness of the penalty dished out to Hamilton in Qatar – a €50,000 fine for a driver allegedly paid $35 million – and the implication that the breach is not as serious as the governing body believes it is.
Similar instances in the past have resulted in fatalities.
In 2014, sprint car driver Kevin Ward Jr was killed when he entered the racetrack after crashing out and was struck by Tony Stewart's car.
More recently, Joe Turney was struck during the FIA Karting World Championship as he pushed his kart in an attempt to rejoin the race following an incident.
While the Englishman survived he has since undergone surgery on his ankle.