The problem
When using Fiona 1.7.1 it no longer lists GeoPackages or ESRI FileGDB as supported drivers. All other drivers are present and correct.
To check the supported drivers execute the following python code:
>>> import fiona
>>> print fiona.supported_drivers
{'ESRI Shapefile': 'raw', 'OpenFileGDB': 'r', 'SUA': 'r', 'ARCGEN': 'r', 'GeoJSON': 'rw', 'Idrisi': 'r', 'GPX': 'raw', 'SEGY': 'r', 'BNA': 'raw', 'AeronavFAA': 'r', 'GPSTrackMaker': 'raw', 'DGN': 'raw', 'PCIDSK': 'r', 'MapInfo File': 'raw', 'DXF': 'raw'}
Solution
The fiona project started to distribute binary using wheel with GDAL support. Due to some license restrictions binaries don't include GPKG or Esri FileGDB. To have the required drivers execute on bash:
pip install -I fiona --no-binary fiona
The command will download source distribution (tar.gz) and compile Fiona which will link to your GDAL installed library.