Polish MEP Janusz Korwin-Mikke made the gesture in July as he spoke against the influx of migrants into the EU.
In October, Italian MEP Gianluca Buonanno wore a Hitler moustache and gave the salute during a debate where the German chancellor was present.
The pair have been fined $3,380 (Â£2,200) and are suspended for 10 days, but can still vote.
The European Parliament Bureau decided on Monday to confirm the sanctions imposed by the parliament's president Martin Schulz earlier this month, a spokesman said.
Mr Korwin-Mikke was protesting against the transportation of migrants across the EU. He said "This time it is 'ein Reich, ein Volk, ein Ticket'" and later made a speech referring to migrants as "human garbage".
Mr Buonanno wore a T-shirt combining the images of Adolf Hitler and Angela Merkel during a debate on the Volkswagen emissions scandal, and a day later gave the Nazi salute with Mrs Merkel and French President Francois Hollande present.
Both MEPs had been involved in this type of incident before, the European Parliament said.
Mr Buonanno tweeted a photograph of himself in the European Parliament on Tuesday, saying: "They banned me but I went in anyway!"
He was embroiled in more controversy earlier this month when he brandished a gun during a TV interview during a row over Italy's self-defence laws and announced he was setting up a fund to help residents in his town buy guns.
Two right-wing MEPs have been suspended from the European Parliament for making Nazi salutes during sessions.