Etchegaray, 87, suffered a broken femur bone and was taken to hospital, Lombardi said.
The woman, whom Lombardi described as "unstable", was detained for questioning by Vatican security police.
She was the same person who tried to jump a barricade to get close to Benedict at last year's Christmas Mass, the spokesman said.
The Vatican later said in a statement that the 25-year-old Italian-Swiss national was taken to an undisclosed medical facility for "necessary treatment".
She was later quoted by La Repubblica newspaper's online edition as saying that she did not want to harm the pontiff.
The report also quoted Cardinal Angelo Bagnasco, archbishop of Genoa and head of the Italian bishop's conference, as saying: "Nothing serious happened. It wasa woman who tried to greet the holy father."
In his message to more than 10,000 people during the Christmas Eve mass, Benedict urged the faithful to put aside the complexities and burdens of daily life and rediscover the simplicity of the Christmas message.
"We live our lives by philosophies, amid worldly affairs and occupations that totally absorb us and are a great distance from the manger," he said.
"In all kinds of ways, God has to prod us and reach out to us again and again, so that we can manage to escape from the muddle of our thoughts and activities and discover the way that leads to him."
Mass was held two hours earlier than the traditional midnight hour this year to ease Benedict's busy holiday schedule.
On Friday, the pope delivered his traditional Christmas message to tens of thousands of pilgrims gathered in St Peter's Square.
He gave blessings in 65 languages from Maltese to Mongolian and urged tolerance for migrants.
"In the face of the exodus of all those who migrate from their homelands and are driven away by hunger, intolerance or environmental degradation," the Roman Catholic Church calls for "an attitude of acceptance and welcome," Benedict said.