Brainstorming is a creative technique used to support productivity and creativity during the idea generation phase of an innovation process. In professional practice, a facilitator structures, regulates, and motivates those behaviors of participants that help maintain productivity and creativity during a brainstorm. Emerging technologies, such as social robots, are being developed to support or even automate the facilitator’s role. However, little is known about whether and how brainstorming with a social robot influences productivity. To take a first look, we conducted a between-subjects experiment (N = 54) that explored 1) whether brainstorming with a Wizard-of-Oz operated robot facilitator, compared to with a human facilitator, influences productivity; and 2) whether any effects on productivity might be explained by the robot’s negative effects on social anxiety and evaluation apprehension. The results showed no evidence for an effect of brainstorming with a teleoperated robot facilitator, compared to brainstorming directly with a human facilitator, on productivity. Although the results did suggest that overall, social anxiety caused evaluation apprehension, and evaluation apprehension negatively affected productivity, there was no effect of brainstorming with a robot facilitator on this relationship. Herewith, the present study contributes to an emerging body of work on the efficacy and mechanisms of the facilitation of creative work by social robots.