Jansson was in clear discomfort during the closing stages of Leeds' 1-0 defeat to promotion rival Sheffield United on Saturday but completed the 90 minutes – remarkably concluding the match as an emergency goalkeeper after Kiko Casilla was sent off.
The 28-year-old centre-back has withdrawn from Sweden's squad for their opening Euro 2020 qualifiers against Romania and Scandinavian neighbour Norway.
"Pontus Jansson will not join up with the Swedish national team during the international break," read a statement from Leeds.
"The centre-back suffered an injury to his knee in Saturday's game with Sheffield United, which will see him sidelined for three weeks.
"Jansson will begin his rehab at Thorp Arch with the Leeds United medical team this week."
Leeds is third in the Championship with eight games remaining, a point behind Sheffield United in the second automatic promotion spot.
Jansson will miss Millwall's visit to Elland Road on March 30, with the subsequent back-to-back away games against Birmingham City and Preston North End his targets for a return.