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To heal or mend, usually of an injury or wound that has broken the skin. The doctor didn't' t give me stitches because he thinks my cut will heal over pretty quickly on its own.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
[for the surface of a wound] to heal. The wound healed over very quickly, and there was very little scarring. I hope it will heal over without having to be stitched.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.