The claim was made by Dortmund chief executive Hans-Joachim Watzke in an interview for a German newspaper.
The 30-year-old moved to Arsenal from the German club for a fee of £56m in January 2018.
“Better for you I never talk about why I really left Dortmund Mr Watzke. You are such a clown,” Aubameyang tweeted.
“I remember that time you said we never gonna sell Ousmane [Dembele], then you saw more than £100m, you were the first to take that money.
“Don’t talk about money please. Leave me alone please,” he added.
Watzke had been talking about the future of England player Jadon Sancho, who is in his third season at Dortmund, when he made this pointed reference about his club’s former player.
He told Suddeutsche Zeitung: “Pierre-Emerick Aubameyang, who plays great at arsenal, will probably be warm-hearted when he looks at his bank account, but on Wednesdays he will be saddened when he has to watch the champions league on television.”
In his reply, Aubameyang referred to the departure of France forward Ousmane Dembele in the summer of 2017, who was sold from the German club to Barcelona for £135.5m.
Since Aubameyang moved to the Emirates he has not played in the champions league, despite ending the 2018/19 premier league season as joint leading scorer with 22 goals alongside liverpool duo Sadio Mane and mohamed salah.
The Gunners have failed to qualify for the Champions League for the past three consecutive seasons.
Dortmund currently top Group F in the competition following a 2-0 win at Slavia Prague on Wednesday.
Arsenal host Belgian side Standard Liege in the europa league on Thursday.