The Poland international, 24, was dismissed for a kick at Hamburg’s Per Ciljan Skjelbred during the surprise 4-1 home defeat last Saturday.
Lewandowski had put the hosts ahead but, after his side slipped 2-1 behind, he appeared to lose his cool with the Norway midfielder, lashing out and receiving a straight red card.
The DFB immediately handed Lewandowski a three-match ban, which Dortmund sporting director Michael Zorc described as “excessive”.
Coach Juergen Klopp added that “many would have said yellow was sufficient, and we think it should be discussed further”.
Lewandowski’s hearing will take place on Tuesday at 16:30 local time (15:30 GMT).
He is the Bundesliga's joint-top scorer with 14 goals this season. Champions Dortmund lie second behind runaway leaders Bayern Munich.