Official milk prices in the Spanish small ruminant sector were used for 5 years (2015–2019) to analyze the effect caused by the coronavirus disease (COVID-19) crisis in 2020. Meat price fluctuations were also studied using the weekly prices officially provided by some of the main agrarian markets of the country (n = 6) in 2019 and 2020. Moreover, the sales and prices of three protected geographical indications (PGI) of lamb meat served to study the marketability when the products are sold or not under these quality labels in a crisis context. According to Spanish Government’s official communications, 2020 was divided in three periods of study (pre-COVID-19, total confinement and post-confinement). The evolution of employment in this subsector in 2020, as a direct consequence of this crisis, was also analyzed considering data provided by producers. Results showed an intra-annual seasonal effect for milk prices in 2020 for both livestock species, as observed in previous years. However, a negative economic impact on goat milk prices due to the pandemic was checked during the confinement and post-confinement months. Sheep milk prices remained stable. Lamb and goat kid meat prices showed a similar trend in comparison with 2019 during the pre-COVID-19 period. The total confinement period recorded a short interval of 1–2 weeks in which the prices declined, before the suspension of quotations in many markets. In contrast, once confinement was completed, meat prices for both ruminant species rapidly reached levels that existed before the coronavirus crisis. Overall data suggested the protective effect of the PGI marks on lamb meat. Lambs with a PGI had better 2020 prices than non-PGI lambs (+8%), regardless of the period analyzed. Moreover, with fewer lambs sold in 2020, there was a relevant drop in sales of non-PGI lambs vs. PGI (−19% vs. −2%) during the first 7 months. Finally, there was little or no readjustment of the workforce in the small ruminant flocks.