Analysis of Pirelli rubber after the opening day of action at the Losail circuit has revealed that there was evidence of a sidewall separation between the topping compound and the carcass cords.
A statement issued by the FIA suggested that this problem could lead to air loss if the tyres were used too much.
Initial indications pointed to the problem having been triggered by a new design of kerbs built in Qatar for this weekend's event.
"This issue has likely been caused by the high-frequency interference between the tyre sidewall and the 50mm 'pyramid' kerbs used extensively at this circuit, aggravated by the propensity to ride those kerbs," explained the governing body.
The issue is enough of a worry for the FIA to prompt an emergency reshuffle of its timetable for Saturday – with an extra practice session now slotted in to evaluate the situation.
In its statement, the FIA said that a host of measures were being taken to avert the possibility of problems in the race.
It explained that track limits at Turns 12-13 would be revised and that an extra 10-minute familiarisation session would take place at 4pm local time on Saturday – shifting back the start of sprint shootout qualifying - to allow drivers to get used to the new policing.
The sprint shootout will now start at 4:20pm local time – 20 minutes later than originally scheduled.
Following the sprint race on Saturday evening, further analysis of the tyres will take place to decide if any more action is needed for Sunday's grand prix.
If there are signs of further trouble, then the FIA could force maximum usage for tyres on Sunday on safety grounds.
This would be that tyre life must not exceed 20 laps for new tyres in the race, and this number would rise to 22 for any used tyres fitted in the race, to account for in-out laps in qualifying.
All drivers would also be obliged to perform at least three tyre-change pitstops during the race.
Ahead of the Qatar Grand Prix, AlphaTauri driver Yuki Tsunoda expressed his concern about the aggressive kerbs that had been introduced this year.
"It's the step between the kerb and off track," he said. "Driving on the kerb won't be an issue, but once you step out from the kerbs it's going to be like a complete sliding effect.
"It is not smooth at all, and especially driving here, with such high-speed corners where the car is really low, it will be hard. Even one time will be pretty costly I think."