The governing International Automobile Federation (FIA) said in a statement that its court of appeal had decided to reduce the sanction to a reprimand and $50,000 fine.
The race ban, handed out by stewards in Hungary last month, had threatened to prevent double world champion Alonso from appearing before his home crowd in Sunday's European Grand Prix.
Renault also argued that the suspension would have "severe consequences" for the local race organisers as well as hitting fans who had bought tickets in the expectation of Alonso racing.
Stewards had punished the team after a wheel came off the Spaniard's car and bounced away to the side of the track during last month's Hungarian Grand Prix.
The incident came a day after Ferrari's Brazilian Felipe Massa had been seriously injured by bouncing debris in qualifying.
It also followed the death of Henry Surtees in a Formula Two race at Brands Hatch after the 18-year-old Briton, son of 1964 world champion John, was hit on the head by a loose wheel.
Renault were accused of releasing Alonso's car after a pit stop, knowing that there was a problem with his right front wheel. The team admitted a breach of regulations but denied deliberate misconduct, with Renault lawyer Ali Malek telling the four appeal court judges that the punishment was both excessive and unfair.
"This case does not deserve more than a reprimand," he added, saying that a ban should be reserved for serious offences such as cheating and conscious wrongdoing. "Was there conscious wrongdoing from Renault? There was none whatsoever," he said.
"The only persons who knew...were the two mechanics," said Malek. "Nobody on the pitwall knew there was a problem and the driver did not know either.
