Rummenigge has been quoted as revealing that Dortmund star Reus has a buy-out clause of €25million written into his contract, which comes into effect next year.
That has led to speculation that Bundesliga champions Bayern may look to snare Reus from their arch-rivals, as they have done with Mario Gotze and Robert Lewandowski in the last two years.
And Rummenigge's claims have irked Watzke, who has criticised his Bayern counterpart for trying to cause disruption at Signal Iduna Park.
"Borussia Dortmund has noted with some irritation that Karl-Heinz Rummenigge is currently discussing internal BVB matters in a three-day rhythm in the media," read a statement from Watzke on Dortmund's official website.
"We are sure that every person interested in football knows what the intention of such statements is.
"Through his conduct, Karl-Heinz Rummenigge is approving that the already tense relationship between Borussia Dortmund and FC Bayern Munich is further damaged.
"We, as an employer, will naturally remain committed to our policy of never discussing contract matters of our employees in the public."
Reus has reportedly attracted interest from several European giants, including Barcelona, Liverpool and Manchester United, after impressing in the past two seasons.
The forward has scored 30 goals in 62 Bundesliga appearances since joining Dortmund from Borussia Monchengladbach ahead of the 2012-13 campaign.