Pere Gratacos lost his main post at the club after saying “it was not only Messi” who got them through a Copa del Rey tie with Athletic Bilbao.
Barca reached the quarter-finals with a 4-3 aggregate win thanks to a 78th-minute Messi free-kick on Wednesday.
Gratacos said: “Messi wouldn’t be as good without Andres Iniesta or Neymar.”
He added: “Obviously Leo is the most important player of the team but it was Luis Suarez and Gerard Pique as well – the whole team – who got us through.”
In a statement on Friday, Barca said Gratacos would be replaced as head of sporting relations with the Spanish Football Federation, but would retain a role within the club’s youth academy.
He made the comments after Barca were drawn to play Real Sociedad in the last eight of the Spanish Cup.
Messi, 29, is yet to agree a new contract with Barcelona, with his deal set to expire in 2018.
The five-time Ballon d’Or winner has been with the Spanish club since he was 13. Speaking in November, club president Josep Bartomeu said he was “convinced” Messi would end his career at Barca.