In most cases, an underwriter will ask for proof that the judgment has been paid prior to or at closing so there isn't a specific amount of time required but a lot of the investors that buy mortgages (actually mortgage backed securities) will require that judgment is either removed from your credit report or shows as paid on the credit report so you could end up with an extra week or two added to the process. Unfortunately, judgments are recorded by your county clerk so any updates will have to go through them first so Lowell's suggestion of getting a letter showing it's paid will not get it deleted from your credit report.
Please feel free to contact me for more information or help.
Senior Mortgage Banker
Peoples Bank & Trust Co.