Watzke insinuated that Aubameyang had joined Arsenal because of money, rather than to better his career.
The 60-year-old also had a not-so-subtle dig at the striker for playing in the Europa League rather than the Champions League.
"Of course it is hard to keep a player in the face of such sums," Watzke told Suddeutsche Zeitung.
"Some go to clubs because of this money, where they have not played Champions League for years.
"Aubameyang, who plays great at Arsenal, will probably be warm-hearted when he looks at his bank account, but on Wednesdays will be saddened when he has to watch the Champions League on television."
Aubameyang has doubled down on his former employer, calling him 'such a clown' in a ruthless tweet posted on his official Twitter page.
The tweet read: "Better for you I never talk about why I really left Dortmund Mr Watzke you such a clown.
"I remember that time you said we never gonna sell Ousmane then you saw more than 100M you were the first to take that money."
Arsenal's golden boot winner from last season refers to Borussia Dortmund's sale of Ousmane Dembele in 2017 in a deal that could yet rise to £135.5 million.
Aubameyang implies that Watzke lied to the team about not selling Dembele, and that he is in fact the one obsessed by money.
The 30-year-old appears to be laughing at Watzke and his comments, judging by his use of emojis.
Aubameyang was an prolific player for Dortmund, scoring 141 goals in 213 appearences for the Bundesliga side.
Since joining the Gunners in 2017 for a fee of £58 million, the Gabonese striker hasn't slowed down in terms of goalscoring - netting 49 goals in 73 games.
His most recent came against Manchester United at Old Trafford which earned Arsenal a 1-1 draw against their old rivals.
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