Production companies throughout the world are currently facing challenges with the extensive transformation of their processes with regard to digitalisation and other features of Industry 4.0. Simultaneously, traditional quality management processes must be significantly changed, and the umbrella term “Quality 4.0” is used to represent this transformation. Many companies, including Czech enterprises, are still struggling with the concept of Quality 4.0, as there are a lot of uncertainties, misunderstandings, and false approaches. Additionally, a lot of questions arise about how to provide an objective and comprehensive assessment of the company’s maturity or readiness for Quality 4.0. Therefore, the main objective of this article is to present our proposal of a framework and methodology on how to assess and measure the maturity level for the implementation of Quality 4.0. This proposal will be supplemented by a presentation of the main results obtained from a special field study, which was conducted at Czech production companies with the aim of obtaining a representative set of information showing their readiness to adopt Quality 4.0 and convert existing quality management systems into the new era. The authors also identify some research gaps, including the necessity to confirm the mutual relationship between the dimensions and items of Quality 4.0 and the sustainable development of companies or society.