© 2018 American Physical Society. We perform the first direct mass measurements of neutron-rich calcium isotopes beyond neutron number 34 at the RIKEN Radioactive Isotope Beam Factory by using the time-of-flight magnetic-rigidity technique. The atomic mass excesses of Ca55-57 are determined for the first time to be -18650(160), -13510(250), and -7370(990) keV, respectively. We examine the emergence of neutron magicity at N=34 based on the new atomic masses. The new masses provide experimental evidence for the appearance of a sizable energy gap between the neutron 2p1/2 and 1f5/2 orbitals in Ca54, comparable to the gap between the neutron 2p3/2 and 2p1/2 orbitals in Ca52. For the Ca56 nucleus, an open-shell property in neutrons is suggested.