The 20-year-old Dembele is seen as a potential successor to Neymar at Barcelona, after the Brazilian's record 222-million euro ($260 million) move to Paris St Germain earlier this month.
German media have reported that Dembele could join Barca for more than 100 million euros but Dortmund said on Thursday an offer made by the Spanish club did not meet their valuation and a move was now unlikely.
Dembele will now miss Saturday's German Cup first round at sixth-tier club Riesalingen-Arlen
"Ousmane Dembele was missing from training (on Thursday) without excuse and obviously took such a step consciously," said Dortmund sports director Michael Zorc in a statement.
"Obviously we will be sanctioning such wrong behaviour. In addition after discussions with the coach we suspended the player from match and training action until next week and after our German Cup game on the weekend."
Dembele joined Dortmund, who will compete in the Champions League group stage, a year ago on a five-year contract.
(Reporting by Karolos Grohmann; Editing by Toby Davis)
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