"Primadonna" has a length of three minutes and thirty-eight seconds. It is a dance-pop song that blends grinding disco and electropop beats with elements of Europop. Diamandis' vocals in the song have been described as operatic. Revolving around an anti-chorus song structure, the chorus is sung in a high tone over sparkly instrumentation before the beat drops to grinding four on the floor verses, where she sings in the gravelly tones of her lower register.

Robert Copesy of Digital Spy rated the track four out of five stars, writing that in the line "Got you wrapped around my finger babe/You can count on me to misbehave", Diamandis "play[s] out one of many female archetypes that feature on her forthcoming LP—though we suspect it's one she identifies with best." Sam Lansky of MTV Buzzworthy described it as "a monster song" and "a muscular uptempo joint", concluding, "Evoking Kate Bush on the high notes and then cascading down to the gravelly tones of her lower register, Marina's voice packs the track with verve and personality." Katherine St Asaph of Popdust gave the song three-and-a-half stars "edging toward 4", referring to it as "a big ball of irony sprinkled with mockery and shoved beneath a blonde wig, roots be damned". On the other hand, Luke Turner of the NME wrote that in the wake of Madonna's contributions, "plonkers like Marina have got empowerment wrong, coming up with this: Europop fart beats and cloying vocals. Marina would do well to learn that ego needs something to back it up, which you won't find in this giant guff of saccharine nothing." Also, Elizabeth McGeown, writing for Irish webzine State, dismissed "Primadonna" as a "wannabe feminist [anthem] disguised in a Mean Girls-esque dialogue. Admittedly, it doesn't take itself seriously. Heavily pop culture laden, it contains a tongue-in-cheek superficiality."

"Primadonna" was well received within the first hours of its release to radio by fans and new listeners alike, especially on the social networking site Twitter where it was a worldwide trending topic.

"Primadonna" debuted at number eleven on the UK Singles Chart with 25,337 copies sold in its first week, giving Diamandis her highest-charting single in the United Kingdom to date and only narrowly missing the top 10 by 525 sales. As of 1 February 2018, the song had sold 300,000 combined units in the UK. As of 5 February 2019, the song has sold 334,000 combined units in the UK. On 9 February 2024, sales and streams of "Primadonna" passed 600,000 units and was awarded a Platinum certification from the British Phonographic Industry. In its third week on the Irish Singles Chart, "Primadonna" rose to a new peak of number three, becoming Diamandis's highest-charting single in Ireland as well. The song peaked at number four in New Zealand, her first single to chart in that country.

"Primadonna" also saw success on pop radio formats in the United States, bubbling under the respective Billboard Pop Songs chart. The song also saw a certain amount of club play, almost charting on the Hot Dance Club Songs chart. In May 2017, "Primadonna" was certified Gold by the RIAA for sales exceeding 500,000 copies. In 2021 it crossed the one million sales mark in the United States and was awarded Platinum.