(1) Background: The impact of the health crisis caused by coronavirus disease 2019 (COVID-19) has provoked collateral effects in the attention to pathologies with time-dependent treatments such as strokes. We compare the healthcare activity of two stroke units in the same periods of 2019 and 2020, with an emphasis on what happened during the state of alarm (SA). (2) Materials and methods. Hospitals in the region implemented contingency plans to contain the pandemic; in this planning, the stroke units were not limited in their operational capacity. The SA was declared on 15 March and remained in place for 10 weeks. For the analysis, the data were grouped by consecutive calendar weeks. (3) Results. When the SA was declared the number of calls to the emergency telephone went from 1225 to 3908 calls per week (318% increase). However, the activation of the stroke code went from 6.6 to 5.0 (p = 0.04) and the activity in both stroke units decreased. The largest drop in hospitalizations was for transient ischemic attacks (TIAs) with 35.7% less, 28 vs. 18, (p = 0.05). Reperfusion therapies fell by 37.5%; Poisson regression model 0.64; (95% confidence interval (CI), 0.43–0.95). The overall activity of the telestroke suffered a reduction of 28.9%. We also observed an increase in hospital mortality. (4) Conclusion. The excessive duration of the pandemic precludes any hope of resolving this public health crisis in the short or medium term. Further studies should be conducted to better understand the multifactorial nature of this dramatic decline in stroke admissions and its negative impact.