It has recently been shown that the mere presence of one’s own smartphone on the desk impairs working memory performance. The aim of this study was to follow up on this important finding by assessing the effect of smartphone presence (present on the desk vs. absent from the desk) on different memory functions (short-term memory and prospective memory), and by further examining the moderating role of individual differences in smartphone dependency and impulsiveness. We found no overall effect of smartphone presence on short-term and prospective memory performance. There was a moderating effect for prospective memory: Performance was better when the smartphone was absent versus present for participants with low smartphone dependency. In light of the absence of an overall effect of smartphone presence on memory functions, our results show that previous findings of impairments in working memory due to smartphone presence do not generalize to other domains of memory capacity.