Portugal's Raphael Guerreiro scored twice to claim all three points for the visitors as Atletico Madrid could only draw 0-0 at Club Brugge.
Lucien Favre made nine changes from Saturday's derby victory against Schalke which continued their superb unbeaten start to the Bundesliga season.
"It's a perfect evening. On the whole it was a deserved victory," Favre said.
Henry started four teenagers in a meaningless game for the Ligue 1 strugglers who were guaranteed to finish bottom of the group for a second straight campaign after defeat at Atletico in round five.
The former France striker stated he used the fixture as a warm-up for Sunday's domestic trip to Lyon.
"Dortmund posed a real challenge. We'll recover quickly and prepare for Lyon," he said.
"Right now we have a problem, to sort things out in Ligue 1."
Monaco have failed to win in 14 European games and the Germans made it through to the knockout stage of the top-tier competition after having to settle for a Europa League place last season.
With a quarter of an hour on the clock the Germans attacked and the ball was worked to striker Maximilian Philipp inside the box.
His low cross found winger Guerreiro at the back post to tap in.
Dortmund centre-back Abdou Diallo, who spent three seasons with the principality outfit earlier in his career, wasted a good chance on the half-hour mark as he scuffed his shot wide despite being unmarked in the box.
In a scrappy second half neither team could muster a clear shot on goal until Guerreiro added his second of the game and fourth in the competition so far this season from a delicate Paco Alcacer lay-off on 88 minutes.
In Belgium it finished goalless between Club Brugge and Atletico and the Germans finished above the Spanish club on their head-to-head record.