Abstract Cell‐based therapies have transformed the treatment landscape for a range of diseases, leveraging both genome modification and cell reprogramming to create targeted treatments. Such therapies rely on the efficient internalization of biomolecules into living cells. Unfortunately, existing cargo delivery methods, such as those based on viral vectors and electroporation, are often compromised by cytotoxicity, poor delivery efficiencies, and low throughput. To overcome these limitations, a viscoelastic squeezing methodology is presented that uses viscoelastic microfluidics to perform mechanoporation in a rapid and contact‐free manner. Through the control of the flow rates of a sample stream containing cells and cargo and a surrounding viscoelastic sheath flow, the width of a “virtual channel” formed between the two streams can be regulated. Elastic forces generated within this virtual channel are then used to deform contained cells and internalize user‐defined payloads. The effectiveness and utility of the platform are assessed through the delivery of mRNA, plasmid DNA, and clustered regularly interspaced short palindromic repeats (CRISPR‐Cas9) ribonucleoprotein complexes into a variety of cell lines. Data confirms that viscoelastic squeezing provides for enhanced delivery efficiencies when compared to conventional poration techniques, whilst maintaining high cell viabilities and throughputs of 20 million cells per minute, and thus represents a powerful tool for cellular engineering.