In the country of Freedonia, wealthy socialite Mrs. Teasdale (Margaret Dumont) agrees to give the small country a sum of $20 million in order to save it from bankruptcy provided that Rufus T. Firefly (Groucho Marx) is appointed the new leader. During the inaugural ceremony, Firefly courts the widowed Mrs. Teasdale and insults her friend Trentino (Louis Calhern), the scoundrelly ambassador of the neighboring country of Sylvania. Firefly then sings out that if Freedonians think that their country is bad off now, "Just wait 'til I get through it with" ('These Are the Laws of My Administration').
Meanwhile, Trentino schemes with the seductive Latina singer Vera Marcal (Raquel Torres), telling her to keep Firefly out of the way while he tries to win Mrs. Teasdale's hand in marriage. Trentino also hires hot dog and peanut vendor Chicolini (Chico Marx) and Firefly's goofy and mute chauffeur Pinkie (Harpo Marx) to spy on Firefly. However, both Chicolini and Pinkie deal with a unfriendly lemonade vendor (Edgar Kennedy) off-and-on who thinks that Chicolini's peanut stand is taking away his business.
Firefly presides over his cabinet. He refuses to discuss taxes or anything else that has to do with the government. He reduces workers hours by shortening their lunch breaks against the protest of his personal secretary Bob Rolland (Zeppo Marx). Next, Firefly hires Chicolini to be his secretary of war, believing he will annoy the rest of the cabinet. Firefly and Bob Rolland decide that they want to start a war with Sylvania by causing a personal feud with Trentino.
At a picnic, Firefly interrupts Trentino's attempt to propose marriage to Mrs. Teasdale. When Trentino calls him an upstart, Firefly slaps him with a glove and declares war between Freedonia and Sylvania. Mrs. Teasdale arranges for the two men to make peace that night. Firefly jokingly asks Trentino what he called him earlier. When Trentino answers "upstart", Firefly slaps him again and once more declares war.
Vera is a guest at Mrs. Teasdale's house. That same evening, she phones Trentino and tells him about her situation and that Firefly is there with Freedona's war plans for Sylvania. Trentino sends Chicolini and Pinkie to the house to steal the war plans. Chicolini locks Firefly in his bathroom and dresses up like him with eyeglasses and a fake thick greasepaint mustache and eyebrows. Pinkie also dresses up as Firefly as well. Both Chicolini and Pinkie try to fool Mrs. Teasdale into giving them the war plans. But Firefly breaks out of his bathroom and attempts to find the men impersonating him. In a famous sequence, Pinkie breaks a large mirror and mimic's Firefly's movements in what is later known as the 'Mirror Sequence'. Firefly is fooled for a time in thinking his look-alike is his reflection until Chicolini shows up and Firefly captures him, while Pinkie flees.
Chicolini goes on trial, but the chaotic proceedings come to a halt when Mrs. Teasdale tells Firefly that Trentino is on his way to the courthouse to make one final effort to avoid war. Firefly agrees to apologize to Trentino for insulting him, but has second thoughts when he considers that Trentino may refuse to shake his hand of friendship. When Trentino enters, Firefly immediately slaps him instead of suffering a possible rejecting and being insulted. Trentino storms out, declaring war. Firefly, Chicolini, Pinkie and Bob Rolland all sing in chorus of the impending war ('The Country's Going To War').
A 'Great War' breaks out between Freedonia and Sylvania. As Firefly receives news and orders from the front lines, an enemy artillery shell destroys part of his headquarters. He then produces a Tommy sub-machine gun but guns down many of his own men. To get new recruits, Pinkie is seen roaming the countryside and battlefields (stock footage from the battles of the first world war) carrying a placard that reads: "Join and Army and See the Navy".
Chicolini shows up at Firefly's headquarters claiming that he just deserted from Trentino's armies and joined Freedonia because they serve better food. Mrs. Teasdale calls Firefly and claims that her house is under attack from enemy soldiers. Firefly, Chicolini, Pinkie, and Bob rush to her aid but they find themselves trapped at the house. Just when it looks like they will be defeated when enemy troops storm the house, they capture Trentino when his soldiers break into the house. The four men pellet Trentino with orange until he gives up. Firefly declares that: "Freedonia has won the war!" They continue to pellet the captive Trentino with oranges and other fruit. In the final shot, when the happy Mrs. Teasdale sings the Freedonia national anthem, the four men pelt her instead.