Arsenal forward Havertz was subbed off in the first half of Thursday's 1-1 draw with the Netherlands in Amsterdam with what appeared to be a hamstring injury.
In a statement, the DFB said he suffered a "muscle strain" but did not indicate how long the 27-year-old was likely to be out of action.
Bayern Muninch's Musiala, 23, was injured in the warm-up on Thursday and took no part in the match.
The DFB said a scan showed a muscle tear in his thigh.
Having initially named two squads as part of a 44-man group for the four international matches, Germany coach Jurgen Klopp has brought in forwards Florian Wirtz and Jonathan Burkardt from the second set-up to replace the duo for Sunday's match against Greece in Augsburg.