The present study focuses on the impact of SARS-CoV-2 (COVID-19) transmission prevention measures and, in particular, home confinement of families with children with autism spectrum disorder (ASD) in Greece. It is assumed that the implemented new measures during the pandemic constitute a profound change for children on the spectrum, considering that the core ASD symptoms include the persistence and adherence to routine and stability, a condition that also directly affects the children’s parents. Semi-structured telephone interviews were conducted. Participants were 10 caregivers with a child diagnosed with ASD of medium or high functioning in Greece. The ages of the children range from 6.5 to 15 years old. The results of the thematic analysis revealed three main themes: (1) the educational framework, (2) the management of daily life, and (3) the construction of the new daily routine. These three themes represent the levels that have undergone a decisive transition, and the sub-themes recommend the areas, individual ways of dealing with this shift. So far, the impact of the pandemic mitigation measures cannot be described as generally positive or negative, as there have been advances and setbacks for children and families alike. Finally, governmental measures and technology-assisted teaching (distance learning) were considered necessary but not sufficient enough for full adaptation.