Quantification of single-cell proteomics provides key insights into cellular heterogeneity while conventional flow cytometry cannot provide absolute quantification of intracellular proteins of single cells due to the lack of calibration approaches. This paper presents a constriction channel (with a cross sectional area smaller than cells) based microfluidic flow cytometer, capable of collecting copy numbers of specific intracellular proteins. In this platform, single cells stained with fluorescence labelled antibodies were forced to squeeze through the constriction channel with the fluorescence intensities quantified and since cells fully filled the constriction channel during the squeezing process, solutions with fluorescence labelled antibodies were flushed into the constriction channel to obtain calibration curves. By combining raw fluorescence data and calibration curves, absolute quantification of intracellular proteins was realized. As a demonstration, copy numbers of beta-actin of single tumour cells were quantified to be 0.90 ± 0.30 μM (A549, ncell = 14 228), 2.34 ± 0.70 μM (MCF 10A, ncell = 2455), and 0.98 ± 0.65 μM (Hep G2, ncell = 6945). The travelling time for individual cells was quantified to be roughly 10 ms and thus a throughput of 100 cells per s can be achieved. This microfluidic system can be used to quantify the copy numbers of intracellular proteins in a high-throughput manner, which may function as an enabling technique in the field of single-cell proteomics.