A biocompatible metal–organic framework MIL-100(Fe) loaded with the active compounds of tea tree essential oil was used to produce composite films based on κ-carrageenan and hydroxypropyl methylcellulose with the uniform distribution of the particles of this filler. The composite films featured great UV-blocking properties, good water vapor permeability, and modest antibacterial activity against both Gram-negative and Gram-positive bacteria. The use of metal–organic frameworks as containers of hydrophobic molecules of natural active compounds makes the composites made from naturally occurring hydrocolloids attractive materials for active packaging of food products.