The age of information (AoI) is a recently proposed metric for quantifying data freshness in real-time status monitoring systems where timeliness is of importance. In this paper, the problem of characterizing and controlling the AoI is studied in the context of blockchain-enabled monitoring networks (BeMN). In BeMN, status updates from sources are transmitted and recorded in a blockchain. To investigate the statistical characteristics of the AoI in BeMN, the transmission latency and the consensus latency are first rigorously modeled. Then, the average AoI, the AoI violation probability, and the peak AoI violation probability are derived in a closed form so as to quantify the performance of BeMN. Furthermore, a simplified form is derived for the AoI violation probability, and it is shown that this quantity can capture the upper or lower bound of the actual AoI violation probability. Simulation results show that each BeMN parameters (i.e., target successful transmission probability, block size, and timeout) can have conflicting effects on the AoI-related performance. Subsequently, design insights are provided to maintain the freshness of the status data in BeMN. Then, experimental results with a real Hyperledger Fabric platform further validate the accuracy of our modeling and analysis.