Can anxiety be caused by not seeing somebody that you really miss?

Anxiety as a process: Anxiety, by definition is a process rather than a discrete emotion that involves cognition (thoughts of uncontrollability & unpredictability of future events), physiological arousal, emotion, and behavior. In other words, the event you mention may "trigger" anxiety in as much as your thoughts about missing someone creates this process. Normal process though unless chronic.

In Short, Yes: Our bodies are desinged to respond in certain ways to certain events. Anxiety in the face of a house fire is great - it makes us get out of the fire! when we have anxiety to something that is not an imminent threat, it can be harmful or troubling. Missing someone (separation anxiety) falls in that category. Our mind knows we shouldn't be anxious but we still feel that way. If extreme, seek help.