Norris was a victim of a sudden power loss after 25 laps at the German Grand Prix and it looked as though another engine, leading to a grid penalty, would have been on the cards.
After analysists from McLaren and Renault looked at it the unit had a minor ancillary failure but is good to go this weekend.
A McLaren spokesperson said to Motorsport.com: "Lando's PU suffered an ancillary failure that forced us to stop the engine.
"We will fit a new design in Hungary. The PU has not been damaged and will be reused in Hungary."
While Norris took penalties in Germany after a new energy store, control electronics and MGU-K the only other element he can replace without a penalty is an MGU-H.
But his teammate Carlos Sainz has reached the limit on all six power unit elements, meaning grid penalties are likely to come during the second half of the season.
McLaren team principal Andreas Seidl said: "Of course, it's a concern, taking all these penalties at the moment, that early in the season.
"But again, we appreciate the ongoing development that Renault is doing in making steps, and of course it's not the target to get all these penalties, but that's the situation that we're in at the moment.
"Hopefully together with Renault, we can improve this situation."