The concept of the stage production is that the audience is watching genderqueer rock singer Hedwig Robinson's musical act as she follows rockstar Tommy Gnosis' (much more successful) tour around the country. Occasionally Hedwig opens a door onstage to listen to Gnosis's concert, which is playing in an adjoining venue. Gnosis is recovering from an incident that nearly ruined his career, having crashed his car into a school bus while high and receiving oral sex from none other than Hedwig. Capitalizing on her notoriety from the incident, Hedwig determines to tell the audience her story ("Tear Me Down").

She is aided and hindered by her assistant, back-up singer and husband, Yitzhak. A Jewish drag queen from Zagreb, Yitzhak has an unhealthy, codependent relationship with Hedwig. Hedwig verbally abuses him throughout the evening, and it becomes clear that she is threatened by his natural talent, which eclipses her own. She describes how she agreed to marry him only after extracting a promise from him to never perform as a woman again, and he bitterly resents her treatment of him. (To further the musical's theme of blurred gender lines, Yitzhak is often played by a female actor.)

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Hedwig tells her life story, which began when she was Hansel Schmidt, a "slip of a girlyboy" growing up in East Berlin. Raised by an emotionally distant single mother after her father, an American soldier, abandoned the family, Hansel takes solace in her love of western rock music. She becomes fascinated with a story called "The Origin of Love", based on Aristophanes's speech in Plato's Symposium. It explains that three sexes of human beings once existed: "children of the Sun" (man and man attached), "children of the Earth" (woman and woman attached), and "children of the Moon" (man and woman attached). Each were once round, two-headed, four-armed, and four-legged beings. Angry gods split these early humans in two, leaving the separated people with a lifelong yearning for their other half. Hansel is determined to search for her other half, but is convinced she will have to travel to the West to do so.

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This becomes possible when, in her 20s, she meets Luther Robinson, an American soldier ("Sugar Daddy") who convinces her to begin dressing in drag. Luther falls in love with Hansel and the two decide to marry. This plan will allow Hansel to leave communist East Germany for the capitalist West. Hansel's mother, Hedwig, gives Hansel her name and passport and finds a doctor to perform a genital reassignment surgery. However, the operation is botched, and Hansel's surgically constructed vagina heals closed, leaving Hedwig with a dysfunctional one-inch mound of flesh between her legs, "with a scar running down it like a sideways grimace on an eyeless face" ("Angry Inch").

Hedwig goes to live in Junction City, Kansas, as Luther's wife. On their first wedding anniversary, Luther leaves Hedwig for a man. That same day, it is announced that the Berlin Wall has fallen and Germany will reunite, meaning Hedwig's sacrifice was for nothing. Hedwig recovers from the separation by creating a more glamorous, feminine identity for herself ("Wig in a Box") and forming a rock band she calls The Angry Inch.

Hedwig befriends the brother of a child she babysits, shy and misunderstood Christian teenager Tommy Speck, who is fascinated by a song she writes with him in mind ("Wicked Little Town"). They collaborate on songs and begin a relationship. Their songs are a success, and Hedwig gives him the stage name Tommy Gnosis. Hedwig believes that Tommy is her soulmate and that she cannot be whole without him, but he is disgusted when he discovers that she is not biologically female and abandons her ("The Long Grift"). He goes on to become a wildly successful rock star with the songs Hedwig wrote alone and with him. The "internationally ignored" Hedwig and her band the Angry Inch are forced to support themselves by playing coffee bars and dives.

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Hedwig grows more erratic and unstable as the evening progresses, until she finally breaks down, stripping off her wig, dress, and make-up, forcing Yitzhak to step forward and sing ("Hedwig's Lament"/"Exquisite Corpse"). At the height of her breakdown, she seems to transform into Tommy Gnosis, who both begs for and offers forgiveness in a reprise of the song she wrote for him ("Wicked Little Town (Reprise)"). Hedwig, out of costume, finds acceptance within herself, giving her wig to Yitzhak. At peace, Hedwig departs the stage as Yitzhak takes over her final song, dressed fabulously in drag ("Midnight Radio").