The meeting, which took place at the Balaidos stadium in Vigo, ended in a 2-0 victory for the guests.
Scored goals were scored by Ansu Fati, as well as Celta's player Lucas Olasa, who scored his own goal.
Since the 42nd minute Barcelona have played in the minority after Clement Lenglet was sent off.
Celta suffered their first defeat this season and have five points after four rounds.
Barcelona won both opening matches. Examples.
Earlier, Barcelona announced Desta's transfer from Ajax.