The governing body will await a report from race organisers about the safety response before deciding if lessons need to be learned.
The scale of the fire that took hold of Webber's Red Bull after its collision with Adrian Sutil led Formula 1 race director Charlie Whiting to order a response vehicle to the incident, anticipating that a vehicle at Turn 3 would be used.
However, there was concern when the fire truck from Turn 1 was dispatched and entered the track ahead of the race leaders - and before the safety car had been able to intervene to slow the field down.
Race winner Sebastian Vettel said: "It wasn't quite clear that it was the safety car but then the safety car board was flashing and I lifted... and obviously saw that there was another car on the track."
Although it is likely that procedures will need tightening for the future, the fact that marshals did wave white flags to warn drivers of the vehicle's presence on track - as is demanded by the International Sporting Code - means the FIA sees no reason for sanctions.
However, race officials always send a report about the events of a grand prix weekend to the governing body, and the FIA is likely to take a more detailed look at what happened to see if there are safety aspects that can be tightened up.
Red Bull boss Christian Horner said the fact that the fire truck was on a long straight was a blessing, as things could have been more dangerous if it had been hidden around a corner.
"It wasn't great, but thankfully it happened on part of the track where there was plenty of time for the drivers to react," he said.
"Sebastian was the first to come across it, but with the straight being so long there he thankfully had enough pre-warning to know that he was there.
"But if it had been unsighted it would have been a bit more dramatic."