As far as I am informed only some banks in Germany will still offer the option to open a 'Mietkautionskonto', but most likely you will need to have a checking account with the bank already.
For instance Sparkasse offers you to open an account specifically for your Kaution for a single payment of 10-30€ (https://www.sparkasse.de/themen/traeume-verwirklichen/mietkaution.html), while DKB offers you a free Kautionskonto as long as you have a checking account with them (https://www.dkb.de/privatkunden/mietkautionskonto/).
Both websites are unfortunately in German, but google translate will likely do the trick or talk directly to a representative for any further questions about details.
Note that the DKB has everything set up online as their main branch is located in Berlin, but customer service online or via phone is spotless. I am myself a customer with them since years and I am very happy.
After you opened the account, you should receive a document from the bank known as 'Verpfändungserklärung' which needs to be signed by your landlord and yourself before handing it back to the bank. This way your landlord will get all information about the account (which runs in your name). All interest earned in the account will be yours, but it's unfortunately not much, so don't get your hopes high.
I hope that helps! Good luck.