Gilbert Arenas -- I Busted My Ex Blabbing About Me ... See Ya in Court, Laura Govan!

Gilbert Arenas caught Laura Govan red-handed leaking their email exchange to a blogger -- and now he's calling her out in front of a judge ... according to court docs.

In the docs filed by the ex-NBA star, he says he has text messages between Laura and the blogger, who last week published details from the emails ... which included allegations of infidelity and domestic violence.

Arenas says Laura violated a court order -- just signed in August -- to keep her mouth shut about him ... when she leaked the email. Specifically, the court order says Laura cannot make "derogatory or disparaging remarks" about Gilbert.

Arenas also accuses Govan of leaking a letter his attorney sent to hers, screwing up their visitation agreement and violating the rules for exchanging their 4 kids.