In general, it is very difficult to measure the information flow in a cellular network directly. In this study, based on an information flow model and microarray data, we measured the information flow in cellular networks indirectly by using a systems biology method. First, we used a recursive least square parameter estimation algorithm to identify the system parameters of coupling signal transduction pathways and the cellular gene regulatory network (GRN). Then, based on the identified parameters and systems theory, we estimated the signal transductivities of the coupling signal transduction pathways from the extracellular signals to each downstream protein and the information transductivities of the GRN between transcription factors in response to environmental events. According to the proposed method, the information flow, which is characterized by signal transductivity in coupling signaling pathways and information transductivity in the GRN, can be estimated by microarray temporal data or microarray sample data. It can also be estimated by other high-throughput data such as next-generation sequencing or proteomic data. Finally, the information flows of the signal transduction pathways and the GRN in leukemia cancer cells and non-leukemia normal cells were also measured to analyze the systematic dysfunction in this cancer from microarray sample data. The results show that the signal transductivities of signal transduction pathways change substantially from normal cells to leukemia cancer cells.