Stuttgart is an environmental zone. This means that your car needs an environmental badge.
Only vehicles in certain emission categories are allowed to drive in the Stuttgart area. This should reduce the excessive fine particulate and nitrogen dioxide levels in the air. This is implemented in Germany in so-called environmental zones.
You can purchase an environmental badge for € 6. You can purchase one directly online or alternatively buy it in person at the Vehicle Registration Office or Citizens' Service Centres. The badges are also available from private organisations and garages (costs may vary and enquiries should be made there).
If you drive into Stuttgart without a green badge, this infringement will cost you € 80.