Would an Antimagic Field block telepathic communication with a familiar?

Ichabod the Inscrutable has an imp familiar and is exploring a dungeon. He comes across a series of trapped rooms that have Antimagic Fields in them, and he wants to send his familiar to explore them.The Antimagic Fields completely fill each room, but do not extend beyond their walls.

Ichabod is currently standing outside of the first room.

Would an Antimagic Field block telepathic communication with a familiar?