Raducanu took a wild card into the low-key Slovenia event and was the top seed but fell to a 7-5 0-6 6-3 defeat in the second round.
The British number one began well and opened up a 5-3 lead in the first set over qualifier Friedsam, who is ranked down at 213, although she has been a top-50 player.
Raducanu then lost four games in a row and began to look uncomfortable in her movement.
She took a medical timeout at the end of the first set and had her left thigh heavily strapped but breezed through the second set only to come up short in the decider.
Raducanu, who is due to play in South Korea next week, saw her ranking plummet to 83 following her first-round US Open loss, but she should regain a few spots courtesy of Monday's win over Dayana Yastremska.
Jodie Burrage was also beaten in the second round, losing 7-5 6-1 to Katerina Siniakova, but Katie Swan reached the first WTA Tour quarter-final of her career with a 7-6 (5) 6-2 victory over Anastasia Gasanova at the Chennai Open.