An inkjet printer is configured with capping stations for storing printheads in the printer during periods of printer inactivity so the viscosity of the ink in the nozzles of the inkjets of the printheads does not increase significantly. Each capping station has a printhead receptacle that encloses a volume, a planar member configured to move between a first position at which the planar member is located within the printhead receptacle and a second position at which the planar member is external of the printhead receptacle, a first actuator operatively connected to the planar member, the first actuator being configured to move the planar member from the first position to the second position, and a controller configured to operate the first actuator to move the planar member from the first position to the second position to mate the planar member with a face of a printhead.