The 31-year-old midfielder was thrilled to hear the Argentina international publicly praise him and stressed that he can become the best player in the history of the game
The Spain international finished third in the poll for the third straight year as Messi picked up the award, while Real Madrid's Cristiano Ronaldo came second.
Upon receiving the prize, Messi paid tribute to Xavi, saying it was "a pleasure" to play alongside the 31-year-old.
"Of course, it [Messi's words] moved me, I liked it a lot," Xavi told Esport3. "It is better than winning an award.
"I did not expect him to thank me. He is a great friend of mine and an amazing person, but he is shy."
Uefa president Michel Platini was coy when asked if Messi could become the best player in football history, but Xavi believes there are no limits to the Argentine's potential.
"It is true that if he continues at this level, he will be the best player ever," Xavi added. "I have no doubt about it.
"He is the one who has to test his own limits. If he continues like this, he will break all records.
"I am happy for him, because he is my friend and also a great guy."
Meanwhile, Andres Iniesta said that Messi is a worthy winner of the Fifa prize, enthusing: "He is a unique player and therefore he deserves to win the Ballon d'Or, just like Xavi does.
"I am happy with it because he is a great team-mate. It is good to be playing with such team-mates.
"[Pep] Guardiola also deserves his award because those who know him know how hard he works.
"The important thing is to keep working. For us there is nothing better."
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