Bora-Hansgrohe rider Sagan was relegated after the sprint finish in Poitiers after he used his head and shoulder to shove Van Aert 50 metres from the line.
The Slovakian, who had finished second on the stage, was pushed back to last place in the peloton, received a fine and was handed a 13 point penalty in the sprints classification by the commissiares.
But the officials also handed a punishment to Jumbo-Visma rider Van Aert, after he made a gesture towards Sagan as the riders crossed the finish line.
After the stage, pictures emerged of Van Aert raising his middle finger to Sagan as he vented his frustration about the incident. You can see the picture on Twitter via Flamme Rouge here
Van Aert was fined 200CHF (£169) for his reaction to the incident, while Sagan was stripped of his second place finish, fined 500CHF (£422) and had 13 points deducted in the green jersey race.
Speaking after the stage, Van Aert said he tried to speak to Sagan but only received “strong words” in response.
The double stage winner in this year’s Tour said: “My opinion is I sprinted in a completely straight line at the right on the barriers.
“He just tried to create space for himself and for me you’re not allowed to do that.
“It’s already dangerous enough. I was really surprised and shocked at that moment, I felt something I was at maximum effort so I was really scared.”
He added: “In the first moment I was so shocked and surprised that I was angry and I used some not very nice words to him. Afterwards I tried to explain it wasn’t right and I didn’t like what he did, but the only thing that came back was other strong words, so it was hard to have a conversation.”