Apart from simple repetition, there is at least one non-fiction book that mentions this anecdote:
There existed at the time a gramophone record of one of Stalin’s longer speeches. It ran to eight sides, or rather seven, because the eighth consisted entirely of applause.
— Martin Amis: "Koba the Dread. Laughter and the Twenty Million", Vinatge Books: London, 2002, p170.
Unfortunately, Martin Amis is not exactly a historian and Koba the Dread falls short on properly referencing this rather vague anecdote.
However, this book is cited or quoted in quite few publications (like this diploma thesis).
A direct proof for this exact claim seems lacking.
Various sites list archives of audio recordings with Stalin's speeches, sometimes with varying for exactly the purportedly exact same speech.
Stalin's ~"Report on the draft Constitution of the USSR November 25, 1936" ("И.Сталин. Речь о проекте Конституции СССР. Доклад на Чрезвычайном VIII Всесоюзном съезде Советов 25 ноября 1936 г.", found in this rar-file) for example lasts for 1 hour and 42 minutes. It starts with ample applause, has especially towards the end some applause sown in, and ends with a full 15 minutes of frenzied ovations that then slowly fades away into singing The Internationale.
Given that recordings on a phonograph record (with 'vinyl' only becoming widespread available very late in Stalin's lifetime) can vary quite a lot:
[…] the early discs played for two minutes […]
with later phonograph/gramophone disc formats by far not approaching the perhaps 'expected' vinyl-LP-recording lengths, the assertion that '(at least) one collection for one of Stalin's speeches had one disc-side that was (at least largely) filled with applause' seems very plausible.