Flow describes a state of intense experiential involvement in an activity that is defined in terms of nine dimensions. Despite increased interest in understanding the flow experience of musicians in recent years, knowledge of how characteristics of the musician and of the music performance context affect the flow experience at the dimension level is lacking. In this study, we aimed to investigate how musicians’ general music performance anxiety (MPA) level (i.e., the general tendency to experience anxiety during solo music performances) and the presence of an audience influence the nine flow dimensions. The participants were 121 university music students who performed solo a music piece once by themselves (private performance) and once in front of an audience (public performance). Their general MPA level was measured with an adapted version of the STAI and ranged from 27 (very low MPA) to 76 (very high MPA). The level of the nine flow dimensions was assessed with the Flow State Scale-2 after each performance. The levels of “concentration on task at hand,” “sense of control,” and “autotelic experience” decreased significantly with increasing general MPA level. The levels of “unambiguous feedback” and “loss of self-consciousness” decreased significantly with increasing general MPA level during the public performance only. The level of “sense of control” was significantly lower during the public performance than the private performance across participants. The level of “unambiguous feedback” was significantly lower during the public performance than the private performance for participants with a general MPA level higher than 47. The level of “loss of self-consciousness” was significantly lower during the public performance than the private performance for participants with a general MPA level higher than 32. In contrast, the general MPA level and the audience did not significantly affect the levels of “challenge-skill balance,” “clear goals,” and “action-awareness merging.” These results show that the effects of general MPA level and audience vary greatly across flow state dimensions. We conclude that musicians’ flow state should be analyzed at the dimension level rather than as a global score. We discuss how our findings could inform the development and implementation of interventions.