One of the main actions implemented globally to control the COVID-19 pandemic has been the restriction of population mobility, by closing borders (aerial, terrestrial and maritime), restricting circulation, and ordering mandatory confinement. Latin America has been no exception, and various countries in the region have implemented, among other measures, border closures and curfew policies. Other countries, such as Mexico, have opted instead for persuasive measures appealing to the good will of the populace, asking them to stay at home and practice frequent handwashing, and have provided the public with daily information regarding the current state of the pandemic. It is to be expected that interventions that fall at either of the two extreme ends of this spectrum lead to different effects on the behaviour of the pandemic. This study aims to analyse the pandemic response measures of border closure and internal mobility restriction, and their relation to the behaviour of the COVID-19 pandemic (by case number trends), comparing Central American countries and Mexico. A document analysis was conducted, using official government publications and mass communication channels that provided information on actions taken to control COVID-19, as well as epidemiological reports from each country. The epidemic curve, which reflects confirmed COVID-19 cases per 100,000 inhabitants, was not significantly different between the Central American countries, which mostly implemented border closures and curfews, and Mexico, which did not. Mandatory border closures and restrictions on internal mobility in Central American countries—with the exceptions of Nicaragua, which imposed neither, and Costa Rica, which imposed border controls but only minimal internal restrictions—were found to constitute human rights violations.