Genetic screening is an advanced tool for reducing recessive disease burden. Nowadays, it is still unclear as to the number of genes or their variants that are necessary for effective screening. This paper describes the development of a carrier screening custom panel for cystic fibrosis, phenylketonuria, alpha-1 antitrypsin deficiency, and sensorineural hearing loss consisting of 116 variants in the CFTR, PAH, SERPINA1, and GJB2 genes. The approach is based on the cheapest and fastest method, on using a small number of genes, and on the estimation of the effectiveness of carriers’ detection. The custom panel was tested on a population-based cohort that included 1244 participants. Genotypes were determined by the TaqMan OpenArray Genotyping platform on the QuantStudio 12K Flex Real-Time PCR System. The frequency of heterozygotes in the Russian population was 16.87% or 1:6 (CI95%: 14.76–19.00% by Clopper-Pearson exact method): in CFTR—2.81% (1:36), PAH—2.33% (1:43), SERPINA1—4.90% (1:20), and GJB2—6.83% (1:15). The data on allele frequencies were obtained for the first time on a Russian population. The panel allows us to identify the vast majority of carriers of recessive diseases in the population. It is an effective approach to carrier screening for common recessive diseases.