In the Industry 4.0 scenario, human–robot collaboration (HRC) plays a key role in factories to reduce costs, increase production, and help aged and/or sick workers maintain their job. The approaches of the ISO 11228 series commonly used for biomechanical risk assessments cannot be applied in Industry 4.0, as they do not involve interactions between workers and HRC technologies. The use of wearable sensor networks and software for biomechanical risk assessments could help us develop a more reliable idea about the effectiveness of collaborative robots (coBots) in reducing the biomechanical load for workers. The aim of the present study was to investigate some biomechanical parameters with the 3D Static Strength Prediction Program (3DSSPP) software v.7.1.3, on workers executing a practical manual material-handling task, by comparing a dual-arm coBot-assisted scenario with a no-coBot scenario. In this study, we calculated the mean and the standard deviation (SD) values from eleven participants for some 3DSSPP parameters. We considered the following parameters: the percentage of maximum voluntary contraction (%MVC), the maximum allowed static exertion time (MaxST), the low-back spine compression forces at the L4/L5 level (L4Ort), and the strength percent capable value (SPC). The advantages of introducing the coBot, according to our statistics, concerned trunk flexion (SPC from 85.8% without coBot to 95.2%; %MVC from 63.5% without coBot to 43.4%; MaxST from 33.9 s without coBot to 86.2 s), left shoulder abdo-adduction (%MVC from 46.1% without coBot to 32.6%; MaxST from 32.7 s without coBot to 65 s), and right shoulder abdo-adduction (%MVC from 43.9% without coBot to 30.0%; MaxST from 37.2 s without coBot to 70.7 s) in Phase 1, and right shoulder humeral rotation (%MVC from 68.4% without coBot to 7.4%; MaxST from 873.0 s without coBot to 125.2 s), right shoulder abdo-adduction (%MVC from 31.0% without coBot to 18.3%; MaxST from 60.3 s without coBot to 183.6 s), and right wrist flexion/extension rotation (%MVC from 50.2% without coBot to 3.0%; MaxST from 58.8 s without coBot to 1200.0 s) in Phase 2. Moreover, Phase 3, which consisted of another manual handling task, would be removed by using a coBot. In summary, using a coBot in this industrial scenario would reduce the biomechanical risk for workers, particularly for the trunk, both shoulders, and the right wrist. Finally, the 3DSSPP software could be an easy, fast, and costless tool for biomechanical risk assessments in an Industry 4.0 scenario where ISO 11228 series cannot be applied; it could be used by occupational medicine physicians and health and safety technicians, and could also help employers to justify a long-term investment.