The decision was made by the regional council on Wednesday.
Parents with prams have previously been allowed to travel for free for safety reasons, so that they would not have to leave their pram while registering their ticket at the front of the bus.
But since SL introduced in August that it is possible to pay at the back on all inner-city buses, the benefit for parents of small children is now also abolished.
It is not clear exactly from which date parents with prams will no longer be allowed to ride the bus for free.
Start the video to hear what toddler parents Hege Gardi and Olivia Nisell think about the decision.