Most articles on the exposure to arsenic (As) associated with rice and rice products come from Asia where these products are consumed in the largest quantities; relatively few of the articles have focused on European consumers. Since rice products can represent a significant contribution to overall arsenic exposure, the aim of the study was to determine the total arsenic content (tAs) in rice and the most commonly-consumed rice products available on the Polish market. The tAs determination was performed by hydride generation coupled to inductively-coupled plasma optical emission spectrometry (HG-ICP-OES). Because an inorganic form of As (iAs) is mutagenic and carcinogenic and about 100-fold more toxic than the organic form, an additional aim of the study was to assess the risk of its ingestion, assuming that it constitutes 67.7%, 72.7%, or 90% of tAs. In all products tested, the calculated iAs content was below the maximum permissible levels, and no threat was found for any of the analyzed Polish consumers, based on the mean rice consumption in Poland and the mean calculated iAs content. However, a potential health risk was noted among infants and young children, assuming maximum iAs levels and threefold higher consumption (16.2 g d−1). To avoid a risk of developing cancer, infants up to one year of age should consume no more than 32.2 g of the studied products per week, children under three years of age up to 68.7 g, and adults 243 g. Consumers should strive to include a variety of cereals in their daily diet and choose products shown to have low arsenic contamination levels based on testing and inspection rankings.