If you actually dial your voicemail (how you do this varies by carrier) you can hear the message and get what is called "envelope information" about the message. To get that info, wait until the message is over and listen closely to the options from the voice prompts. If the caller hasn't blocked their number, you should be able to get it from there.
Side note - is it possible you have this person in your contacts? If you're using a visual voicemail system of some kind it should show what number or contact left the message.