Background Depression during pregnancy and in the postpartum period is associated with poor outcomes for women and their children. Although effective interventions exist for common mental disorders that occur during pregnancy and the postpartum period, most cases in low- and middle-income countries go untreated because of a lack of trained professionals. Task-sharing models such as the Thinking Healthy Program have shown potential in feasibility and efficacy trials as a strategy for expanding access to treatment in low-resource settings; however, there are significant barriers to scale-up. We address this gap by adapting Thinking Healthy for automated delivery via a mobile phone. This new intervention, Healthy Moms, uses an existing artificial intelligence system called Tess (Zuri in Kenya) to drive conversations with users. Objective This prepilot study aims to gather preliminary data on the Healthy Moms perinatal depression intervention to learn how to build and test a more robust service. Methods We conducted a single-case experimental design with pregnant women and new mothers recruited from public hospitals outside of Nairobi, Kenya. We invited these women to complete a brief, automated screening delivered via text messages to determine their eligibility. Enrolled participants were randomized to a 1- or 2-week baseline period and then invited to begin using Zuri. We prompted participants to rate their mood via SMS text messaging every 3 days during the baseline and intervention periods, and we used these preliminary repeated measures data to fit a linear mixed-effects model of response to treatment. We also reviewed system logs and conducted in-depth interviews with participants to study engagement with the intervention, feasibility, and acceptability. Results We invited 647 women to learn more about Zuri: 86 completed our automated SMS screening and 41 enrolled in the study. Most of the enrolled women submitted at least 3 mood ratings (31/41, 76%) and sent at least 1 message to Zuri (27/41, 66%). A third of the sample engaged beyond registration (14/41, 34%). On average, women who engaged post registration started 3.4 (SD 3.2) Healthy Moms sessions and completed 3.1 (SD 2.9) of the sessions they started. Most interviewees who tried Zuri reported having a positive attitude toward the service and expressed trust in Zuri. They also attributed positive life changes to the intervention. We estimated that using this alpha version of Zuri may have led to a 7% improvement in mood. Conclusions Zuri is feasible to deliver via SMS and was acceptable to this sample of pregnant women and new mothers. The results of this prepilot study will serve as a baseline for future studies in terms of recruitment, data collection, and outcomes. International Registered Report Identifier (IRRID) RR2-10.2196/11800