Revealing footage from election night in June 2017 shows Mr Kinnock being told off for agreeing to a television interview shortly after the exit poll.
His wife, the former prime minister of Denmark, Helle Thorning-Schmidt, gives him a reality check moments before he is set to go on the BBC.
The Labour MP was feeling confident as it appeared he had kept his seat, while a shock exit poll showed Jeremy Corby’s left-wing party had done better than expected.
He had previously dismissed Labour’s chances in the snap poll.
Ms Thorning-Schmidt, wearing a red Labour rosette, is shown asking her husband: “Why are you doing this now? Why? What are you going to say?”
The dumbstruck MP for Aberavon replies: “Umm… I don’t know.”
She tells him not to speak about Labour’s success until the result becomes totally clear, in case he is embarrassed.
The Dane says: “Yes, you should wait. You don’t know anything. It looks like we’ve had really good turnout here, which is amazing.
“Just talk about this: it looks like turnout is up here, I’m hoping lots of young people have come out to vote, I’m hoping this will be a new chance for Labour.
“Just keep it to the campaign – nothing about what you thought Jeremy would say. Just keep it simple.”
The footage was broadcast as part of BBC documentary Labour: The Summer that Changed Everything.
Polls in the run-up to the snap election announcement in April predicted a landslide victory for Mrs May, with a majority of as many as 80 seats.
However in a shock twist she actually ended up losing seats, and the confidence of much of her party.