Her aide said he was unaware if Mr Michel had apologised for his part in the gaffe, which has been dubbed “Sofagate”.
The spokesman said Mrs von der Leyen was “surprised” by the two men’s actions.
In video footage of the incident, she, the EU’s first female president, appeared annoyed at the beginning of the bloc’s talks with President Erdogan.
As the Turkish leader took his seat alongside Council President, Mrs von der Leyen gestured at the lack of a third chair.
“Ehm,” she muttered, as the two men settled down at the head of the room hosting the meeting at the presidential complex in Ankara.
Mr Michel, who appeared to make a bee-line for the top seat alongside President Erdogan, offered little in the way of an apology.
The awkward moment came ahead of a three-hour meeting, during which the trio discussed Turkey’s withdrawal from the Istanbul convention on gender-based violence.
Mrs von der Leyen refused to acknowledge the diplomatic blunder in a post-meeting news conference.
She said: “We have come to Turkey to give our relationship a new momentum and in this respect we had an interesting first meeting with president Erdoğan.”
The former German defence minister said Turkey had sent a “wrong signal” by leaving the convention aimed at preventing violence against women.
“I am deeply worried by the fact that Turkey withdraws from the Istanbul convention,” she added.
Dutch MEP Sophie in ’t Veld added: “And no, it wasn’t a coincidence it was deliberate.”
Mr Michel’s office has refused to comment on the diplomatic farce.
Under the EU’s treaty, both the presidents of the Commission and Council should be treated with equal standing on foreign visits.