Alongside Haas' Nico Hulkenberg, Alpine driver Ocon had completed the entire race on the hard tyre, hoping for a late red flag to give him a free, mandatory swap to a different compound.
When that red flag didn't arrive, Ocon waited until the start of the final lap to dive into the pits and pick up soft tyres.
But with race leader Sergio Perez about to cross the line to take the win in Baku, various paddock members were already gathering at the top three parc ferme area at the entrance to the pits when Ocon entered the pitlane, with several people having to duck out of the Frenchman's way.
The incident wasn't helped by the blind approach to the pit entry, with drivers first having to navigate a chicane so Ocon couldn't see what was transpiring until right before the pit entry line.
Soon after the chequered flag, the FIA announced it was looking at what happened, with a spokesperson confirming "We're currently investigating the incident in the pitlane on the final lap."
The FIA then summoned its own staff responsible for managing the parc ferme area with the following statement.
"Representatives of the FIA responsible for the parc ferme area at pit entry are required to report to the Stewards at 17:30."
Afterwards, Ocon said it was a "crazy moment" that could have ended in disaster.
"That is not something that we want to see," Ocon said.
"I don't understand why we are starting to prepare the podium and the ceremony when we are still racing, there is one lap to go and there are still people who didn't pit.
"Arriving at 300 km/h, braking very late and I see the barriers and the people all around. This is crazy, it could have been a big, big one today.
"It's definitely something that needs to be discussed as it is something we don't want to see.
When asked how close Ocon came to hitting someone, he replied: "Well, quite close, I had to lift off, I had to back off, so I would not have liked to have been the ones in the middle there.
"If I miss the braking point, it is a big disaster, so that is a crazy moment."
