Warren Sapp has BLOWN one of the greatest plea deals ever -- AZ prosecutors are gunning to put him IN JAIL for breaking their deal in his hooker case by getting charged with domestic violence in Vegas ... TMZ Sports has learned.

We broke the story ... Sapp cut a huge deal with prosecutors in AZ after he was busted with prostitutes in February in which he agreed to complete various counseling programs and stay out of trouble, and in exchange the charges would be thrown out.

Problem is ... the agreement specifically states that if he gets charged with ANY OTHER crime while enrolled in the program, the deal is off and Sapp would get 30 days in jail and 24 months probation.

Fast forward to Vegas ... where Sapp was just charged with 3 counts of domestic violence for allegedly beating up his longtime girlfriend stemming from an incident in April.

AZ prosecutors took notice ... and this week, they filed new court docs seeking to hold Sapp responsible -- looking to enforce the terms of the Arizona sentence, ASAP.

Now it's up to the judge to sign off on the request ... which means Sapp could be headed to the clink in the very near future.

Stay tuned ...