Ibrahimovic, whose comments were caught on camera, insulted referee Lionel Jaffredo and one of his assistants, then used an expletive to describe France.
Initially talking to the fourth official, he appeared to have said: "F--ing wake up -- we're not playing in the amateurs. Wake up! I have never seen that in 15 years in my career, such a referee in this s--- country. [You] don't even deserve PSG to be in this country."
Ibrahimovic, who later said he was sorry after the French sports minister asked him to apologise, is available for Saturday's Coupe de la Ligue final against Bastia as his suspension starts next week.
Ibrahimovic, who took his tally with PSG to 102 goals in less than three years following his hat-trick in a 4-1 win over Saint-Etienne in the Coupe de France midweek, will also miss the first leg of his club's Champions League quarterfinals against Barcelona after he was sent off against Chelsea in the previous round and suspended for one match.
Although PSG sporting director Olivier Letang argued that Ibrahimovic should not be suspended because he did not address his comments directly to the referee, the disciplinary commission activated a suspended one-match ban imposed following an altercation with a Saint-Etienne player in January to add to the three games he received for the latest incident.
"He has been sanctioned because of the offensive nature and rudeness of his words," said commission president Sebastien Deneux, adding that Ibrahimovic's absence at the hearing did not affect the outcome.
Ibrahimovic's comments in Bordeaux caused an outcry in France, with National Front leader Marine Le Pen suggesting that he should leave the country if he was not happy.
The Swede's suspension is a tough blow to PSG's ambitions as Laurent Blanc's team chases an unprecedented quadruple with a squad already missing several key players through injuries.
Ibrahimovic has been in tremendous form recently, completing two hat tricks in three games and scoring 10 goals in his last six matches for club and country.
The 33-year-old Ibrahimovic has never been shy of controversy during his much-traveled career. After he was sent off for a late challenge on Oscar in the first half of PSG's match at Stamford Bridge last month, he described the Chelsea players as a bunch of "babies."