The 38-year-old succumbed to a 7-5, 7-5 defeat in 100 minutes of play after a close encounter at the 02 Arena.
Thiem came into this match as one of the few players in the game boasting a favourable head-to-head record with Federer, winning four of their six meetings and both matches in 2019.
But Federer prevailed in this fixture at the ATP Finals last year and his stellar indoor record looked as if it would serve him well once again.
But the Swiss veteran got off to a rocky start, finding himself a break down in the maiden game of the match before Thiem consolidated it with a confident service game.
He kept that lead until Federer came fighting back to take three games in a row. It appeared to be heading for a tiebreak at 5-5 until Thiem made him pay for one too many unforced errors and served out the set at 7-5.
Federer began the second set in better shape, winning three consecutive service games, but failed to take advantage of a crucial break point in the fourth. Instead, a resilient Thiem fought hard to keep his lead in tact.
With still no break in sight at 5-5, Thiem stepped things up a gear with some phenomenal shots into the corner. Federer was beginning to look weary and when his backhand volley landed out, Thiem had a triple break point.
The world number five fought hard and eventually, Federer swung one into the net. He was really up against it and even a break would force a tiebreak.
But like a man possessed, Thiem refused to back down – even when Federer began to pull out the shots that only a 20-time Grand Slam winner is capable of.
When finally presented with the match point, Thiem made a hash of it and Federer saw the curtains open once again. He worked hard to find a second break point of the set, but more fine work from Thiem allowed him to keep Federer at an arm’s distance.
At the second time of asking, Federer’s return landed into the net and Thiem had done it. A rocky start to the tournament for Federer, who now has it all to do to qualify from his group and still has to face Novak Djokovic.