On a Blockchain network, transaction data are exposed to all participants. To preserve privacy and confidentiality in transactions, while still maintaining data immutability, we design and implement FabZK. FabZK conceals transaction details on a shared ledger by storing only encrypted data from each transaction (e.g., payment amount), and by anonymizing the transactional relationship (e.g., payer and payee) between members in a Blockchain network. It achieves both privacy and auditability by supporting verifiable Pedersen commitments and constructing zero-knowledge proofs. FabZK is implemented as an extension to the open source Hyperledger Fabric. It provides APIs to easily enable data privacy in both client code and chaincode. It also supports on-demand, automated auditing based on encrypted data. Our evaluation shows that FabZK offers strong privacy-preserving capabilities, while delivering reasonable performance for the applications developed based on its framework.