The Briton's podium finish was confirmed after a six-hour wait following the race on Sunday after stewards had summoned BAR representatives and weighed the car with and without fuel.
"The FIA is to appeal against the decision of the stewards at the 2005 San Marino Grand Prix to take no further action in respect of car number three," an FIA statement said on Monday.
"The international court of appeal is scheduled to hear the case on May 4."
The stewards said on Sunday that Button's car was above the minimum weight limit immediately following the race but that it was underweight after being drained of fuel.
After speaking to BAR and examining all available documentation the stewards decided no further action was required.
In a statement on Monday BAR said it was surprised by the FIA's appeal and that the car had been above the minumum weight at all times during the race.
"BAR will provide the same rigorous data presented to the stewards last night (Sunday) and is confident that it can prove once again that the car was fully compliant with the FIA Technical Regulations throughout the San Marino Grand Prix," BAR Chief Executive Nick Fry said.
Button's podium finish was BAR's first of the season after three races without points.
If he is disqualified, McLaren's Alexander Wurz would be promoted to third and Williams' Mark Webber would move up into the points in eighth.
The next race in the Formula One calendar is the Spanish Grand Prix in Barcelona on May 8.
