Michael Strahan, Nicole Murphy -- Engagement OFF

Michael Strahan and Nicole Murphy have called off their engagement ... just one day before he's inducted into the Pro Football Hall of Fame.

Strahan's rep says it's all about 2,475 air miles -- he lives in NYC and she's in L.A. and it's just too difficult. It's especially hard because they're both real busy.

Murphy was married to Eddie Murphy ... and Strahan divorced Jean Muggli in 2006.

We shot the "Hollywood Exes" star last month after Strahan was threatened by a homeless guy with a knife -- and she seemed in the dark. Now we know why.