The England player was taken off in the 70th minute at Wembley on Wednesday after a tussle left him needing stitches around the top of his left eye.
Danny Rose made just four appearances this season, and only one EPL start, after losing his place to Ben Davies.
Rose played 90 minutes for the first time since January against Dortmund after spending nine months out with a knee injury.
Rose was not even named on the bench for the 2-0 defeat against Arsenal on Saturday, with Spurs the boss saying he still needs to regain fitness.
Tottenham and England full-back Danny Rose used a psychologist during his long injury lay-off as he battled jealously and anger on the road back to fitness.
Danny Rose and Erik Lamela are back in training with the Tottenham Hotspur first-team squad after long injury lay-offs.
Tottenham defender Danny Rose has apologised for an outspoken interview he gave ahead of the new Premier League season.
Tottenham's start to the season has been overshadowed by Danny Rose's criticism of the club's transfer policy.