A video of Williams' gracious act was posted to the Rugby World Cup Twitter page, where fans praised the 34-year-old's gesture.
"One of the classiest players to ever grace the pitch! Always an amazing watch!" one fan wrote.
"What a guy!!! Huge respect," wrote another.
In 2015, Williams made headlines for similar reasons when he gave his World Cup gold medal away to 14-year-old Charlie Line.
Line was tackled by a security guard as he ran on the pitch during the All Blacks' lap of honour.
Williams hugged the boy and walked him back into the stands where he took off his medal and hung it around Line's neck. Williams later said he felt sorry for the "little fella" and that he wanted to make the night more memorable for him.