
The incident occurred late in United's 4-0 FA Cup victory Saturday, when Arsenal were clearly irritated by what they saw as showboating by the Portuguese winger.
An FA spokesman said: "Having viewed the footage, the referee was not satisfied that it showed evidence of violent conduct and therefore no further action will be taken."
United manager Sir Alex Ferguson had attacked Gallas over the incident.
"I thought Gallas should have been sent off," he said.
"The referee must have a look at that again.
"He kicked Nani from behind and the referee called both over because they sized each other up.
"He should have been red-carded."