Jansson has yet to start any of United's three Championship encounters so far this term with the defender having made a late return to training following his exploits with Sweden in the World Cup.
The defender bagged his first minutes of the season when playing the full 90 minutes of United's Carabao Cup clash at home to Bolton Wanderers last Tuesday evening which resulted in a 2-1 victory.
But Gaetano Berardi has instead partnered captain Liam Cooper at the heart of the Leeds defence in United's three league games - with Jansson back on the bench as Cooper and Berardi played the full 90 minutes at centre back of Saturday's 2-0 win at home to Rotherham United.
Jansson was brought on as an 89th-minute substitute for Mateusz Klich against the Millers but Whites head coach Marcelo Bielsa has revealed that the defender then suffered a setback in training that will rule him out of the Championship visit to Swansea.
The Whites head coach will then take a look later in the week to see whether or not Jansson will be ready for Saturday's Championship fixture at Norwich City.
"Jansson won't play tomorrow," said Bielsa.
"He felt something in his back in training. This problem he has doesn't allow him to play tomorrow. We'll see if he can play Saturday."
Asked what he had thought to Berardi's performances at centre-back - with the 29-year-old more naturally recognised as a full back - Bielsa said: "In the games I watched (last season) he played more as a full back than a centre back. Obviously he can play on both sides. As a centre back I have been satisfied with his performance."
Stuart Dallas (quad injury) and Adam Forshaw (damaged foot ligaments) are United's other absentees through injury for the trip to Swansea.
Striker Kemar Roofe is fully fit despite requiring an ice pack on his leg following Saturday’s win against the Millers.
“He has trained normally,” revealed Bielsa.