It's a phase. My daughter went through the SAME thing! It upset so many of our extended family etc.
I would say just give it time. Your daughter is scared, and the worst thing you could do is not acknowledge that. Help her feel secure, don't laugh, get mad or ignore it. Talk in a gentle voice, hold her and assure her that it's ok "Mommy's here". Smile and explain to the individual that it's just a phase, she'll get over it and love you before you know it!
Just let your daughter know you will protect her no matter what. Even when we feel their fears are a bit "silly", they are very much real to them. :)