Pellegrini made a series of complaints about Swedish official Jonas Eriksson after his side were beaten 2-0 by the Spanish champions at the Etihad Stadium last week.
In imposing the sanction, European governing body UEFA also announced that a further one-match ban would be suspended for two years.
Pellegrini appeared to question the integrity of Eriksson as he launched into an astonishing attack on the Swede in the post-match press conference.
Pellegrini felt the offence occurred outside the area and that Jesus Navas was fouled in the build-up.
The City boss said Eriksson was "not impartial" and then asked why a referee from Sweden had been appointed to such a high-profile fixture.
The Chilean also suggested Eriksson may have been trying to make amends for perceived injustices against Barca in a previous game.
Pellegrini said after the game: "From the beginning I felt the referee was not impartial to both teams so he decided the game with a foul that he didn't whistle against and a penalty with Demichelis that was not a penalty, it was outside the box.
"I think it was not a good idea to put a referee from Sweden in charge of such an important match, especially a referee who has made an important mistake against Barcelona in a previous match."
Pellegrini apologised for his remarks two days later, particularly the comment about Eriksson's nationality, which he admitted was a mistake.
"I am sure this is a good referee because UEFA is always evaluating all the referees and if he is not a good referee, he is not in the UEFA staff," the 60-year-old said.
"The thing I said in that moment doesn't mean what I think."
His climbdown did not prevent UEFA charging him with a breach of their disciplinary regulations and the case has now been found against him.
He will now not be permitted in the tunnel, dressing room or technical area before or during the return match against Barcelona on March 12 or their next game in Europe after that.
He will be allowed to watch from the stands but must not communicate directly or indirectly with any player or member of his technical staff.
A statement from UEFA read: "UEFA's control and disciplinary body has suspended Manchester City FC manager Manuel Pellegrini for three UEFA competition matches, one of which is under probation for two years.
"The sanction is due to the coach's press statements and violation of the general principles of conduct under Article 11 of the 2013 UEFA Disciplinary Regulations (DR) at the UEFA Champions League round of 16 first leg between Manchester City and FC Barcelona on February 18 in England."
Pellegrini does have the right of appeal.