The 22-year-old Argentina forward single-handedly destroyed Arsenal's European dreams with all four goals in Barcelona's Champions League quarter-final second-leg victory over the English club at the Nou Camp, which set up a clash with Jose Mourinho's Inter Milan.
"Leo is on another level completely from every other player in the world, in a different class," Xavi declared.
"If you are lucky, you might find a player like this coming along once every quarter of a century."
Barcelona, who had thrown away a two-goal lead in the first leg, were stunned by a shock opener from Nicklas Bendtner on 18 minutes.
However, the visitors' lead did not last long before Messi slammed in a 20-yard drive in a sign of things to come.
Xavi was captain for the night in the absence of suspended Carles Puyol.
With Gerard Pique also serving a one-match ban, and striker Zlatan Ibrahimovic missing because of a calf problem, Spain international Xavi praised the team's efforts.
"In general lines we did everything well," Xavi said on www.uefa.com.
"We were ordered in defence, our technical level was spectacular, we produced individual moments of brilliance and even when Arsenal were good enough to press us back, at times, we knew how to escape and keep on creating."
Defender Daniel Alves believes Pep Guardiola's side are reaping the benefits of approaching the game in the right spirit.
"You start playing football as a kid because you dream of playing on nights like this," Alves said.
"If you love football, like we do, then it's about quality, good play, inspirational performances, and we were magnificent against a tough opponent."
Before thought of Inter and a reunion with their former club translator, however, there is the small matter of Saturday's "El Clasico" clash against Real Madrid.
Barcelona head to the Bernabeu in second place on goal difference, with eight games to go.
Full-back Eric Abidal will, however, miss the trip to Madrid after aggravating a thigh injury against Arsenal.
A statement on Barcelona's club website read: "Abidal suffered a recurrence of the thigh injury he suffered in February as scar tissue ripped, and is expected to be out for up to 10 days.
"The injury means the French full-back will definitely miss this weekend's clash against Real Madrid and next Wednesday's La Liga game against Deportivo, but he could be fit to reappear in the derby game against Espanyol or in the first leg of the Champions League semi-final against Inter Milan set for April 20."