No, it's not necessary to learn music theory to start learning piano. To learn how to play the piano, you really just need to know how to read music, as well as scales and arpeggios. It is good, though not necessary, to know the circle of fourths/fifths as well as how scales are built.
One thing that might be necessary but is so extremely basic that I don't think it counts as music theory would be learning how many sharps and flats go with each scale, so you can recognize what key a piece is in by the key signature.
Music theory is not necessary, but can help you a lot with understanding music that you play. To start with some basics, you could learn different chords (ex. tonic, subdominant, dominant, diminished sevenths) and cadences (interrupted, perfect, imperfect, etc).
You should definitely learn the different periods of music and the characteristics of each (renaissance, baroque, classical, romantic, impressionistic, neo-classical, modern, etc...), as well as different composers. Those really help with understanding the music.