The BAR team has been banned for two races for running an underweight car at the San Marino Grand Prix.
Button will miss the Barcelona and Monaco races
An appeal court of motorsport's ruling body the FIA also stripped BAR of the 10 points won by Jenson Button and team-mate Takuma Sato at Imola.
But it stopped short of meeting the FIA's request that BAR be thrown out of the Formula One championship.
Button and Sato will now have to sit out Sunday's Spanish Grand Prix and the Monaco Grand Prix on 22 May.
And the decision to exclude BAR's San Marino results means the team and its drivers will have no points when they return for the European Grand Prix at the Nurburgring on 29 May.
A further six-month ban has been suspended for a year.
The ruling was the toughest sanction taken against a Formula One team for 20 years.
BAR have reacted angrily and say they are considering an appeal.
"BAR Honda is appalled at the decision and asserts that the judgment is contrary to all of the evidence heard.
"The team proved it complied with the current regulations and the FIA now acknowledges that the regulations are unclear," said BAR team boss Nick Fry
Button took third place behind Renault's Fernando Alonso and Ferrari's Michael Schumacher at Imola, while Sato finished fifth.
It was the first time either BAR driver had finished a race this season.
But Button's car was examined after the race and found to have a secondary fuel tank, which when drained left the BAR 5.4kg under the minimum weight limit.
He was confirmed in third place by the stewards but the FIA appealed against the decision, arguing that BAR had deliberately broken rules by using fuel as ballast to allow the car to run light during the race - giving it a speed advantage.
The four-judge panel announced its verdict in Paris in a seven-page document and stopped short of finding BAR guilty of deliberate cheating.
"The presentation of the team of fuel consumption data cannot guarantee that the vehicle complied at all times with the minimum weight requirements," it said.
"It is not possible for the court to find, on the basis of the evidence that it was provided with, that Lucky Strike BAR Honda deliberately committed fraud."
But the court decided that BAR's decision not to ask for clarification as to whether their system was legal amounted to "a highly regrettable negligence and lack of transparency".
Five Live motor racing commentator Maurice Hamilton, in Barcelona for this weekend's Grand Prix, said:
"What they are saying is that they cannot prove there was a deliberate attempt to cheat but neither did the team prove to the scrutineers and the FIA that the car remained above the 600kg weight limit through the entire race.
"On that basis the penalty is about right because if they had been found guilty of deliberately cheating they would definitely have been excluded from the entire 2005 World Championship."
FIA president Max Mosley said: "The facts in this case are very clear.
"The team was asked to pump the fuel out of their car. They left 15 litres in the tank and told us it was empty.
"Under the circumstances, we feel they have been treated rather leniently."
The exclusion of Button and Sato changes the San Marino finishing order.
McLaren's Alex Wurz, who was racing as a replacement for the injured Juan Pablo Montoya, is elevated to third.
Sauber's Jacques Villeneuve is now fourth, Toyota's Jarno Trulli fifth, Williams pair Nick Heidfeld and Mark Webber sixth and seventh, and Red Bull's Vitantonio Liuzzi eighth.