The blow resulted in a double fracture to Grosso's face.
Tu'ungafasi's shoulder hit Grosso flush on the head in the same tackle that the Frenchman suffered a high shot from All Black Sam Cane resulted in France's only try scorer to leave the field in the second half.
He was taken to hospital as a result and has been ruled out of the remainder of the series with his injuries.
Tu'ungafasi wasn't cited immediately after the test.
"Having reviewed all available camera angles, the Citing Commissioner considered Ofa Tu'ungafasi to have executed a dangerous tackle "just short of" red card level [in accordance with World Rugby Regulation 17], which caused injury to France winger Remy Grosso," a World Rugby statement said.
"In considering the mechanics of the incident, the Citing Commissioner determined that there were mitigating factors which prevented the conduct from reaching the red card level in his opinion. These included Remy Grosso's body position lowering as he went into contact with Sam Cane, who effected the tackle initially, immediately before Ofa Tu'ungafasi joined a dynamic tackle situation.
"As a result, the independent Citing Commissioner issued a Citing Commissioner Warning – issued for acts of foul play that are viewed by the Citing Commissioner to come close to but do not warrant the player receiving a red card."
The Citing Commissioner also said that Cane's initial high tackle on Grosso was worthy of a penalty and no further punishment.
Tu'ungafasi apologised to the Frenchman after the test, stating it was unintentional.
"Remy, I hope you're recovering well. It was a physical game and it wasn't my intention to hurt you," he wrote on Twitter.
"I'm also gutted that I didn't get to see u after the game and u weren't well for me to visit u in hospital this morning before we left but I hope to catch up soon brother (sic)."