(1) Background: Evidence-based policymaking requires data about the local population's socioeconomic status (SES) at detailed geographical level, however, such information is often not available, or is too expensive to acquire. Researchers have proposed solutions to estimate SES indicators by analyzing Google Street View images, however, these methods are also resource-intensive, since they require large volumes of manually labeled training data. (2) Methods: We propose a methodology for automatically computing surrogate variables of SES indicators using street images of parked cars and deep multiple instance learning. Our approach does not require any manually created labels, apart from data already available by statistical authorities, while the entire pipeline for image acquisition, parked car detection, car classification, and surrogate variable computation is fully automated. The proposed surrogate variables are then used in linear regression models to estimate the target SES indicators. (3) Results: We implement and evaluate a model based on the proposed surrogate variable at 30 municipalities of varying SES in Greece. Our model has $R^2=0.76$ and a correlation coefficient of $0.874$ with the true unemployment rate, while it achieves a mean absolute percentage error of $0.089$ and mean absolute error of $1.87$ on a held-out test set. Similar results are also obtained for other socioeconomic indicators, related to education level and occupational prestige. (4) Conclusions: The proposed methodology can be used to estimate SES indicators at the local level automatically, using images of parked cars detected via Google Street View, without the need for any manual labeling effort.