The paper studies the reproductive intentions of the Russians who already have at least one child before and during the quarantine restrictions (lockdowns) due to COVID-19. Binary choice logistic models and a set of machine learning models were evaluated on the data from the Person, Family, Society survey conducted in March—May 2020. Modeling of the respondents’ intentions to have more children in the short term (3 years) and the long term (more than 3 years) showed that external shocks such as the COVID-19 pandemic and the strict quarantine regulations associated with it had an impact on fertility intentions, but only in the short term. These external shocks were less significant than such factors as age of the respondent; the number of children already born; availability of housing needed to expand the family; the maternity capital program availability, which includes the opportunity to improve housing conditions after the birth of children. As Russians with children showed the increase of the probability of having additional children after April 2020, we conclude that the effect of COVID-19 on reproductive intentions was acyclical. The estimation of models with heterogeneous effects showed that the pandemic had a stronger impact on respondents with above-average household incomes.