DepoProvera contraceptive shot stays in your system for 3 months (for protection against pregnancy). That is why after the 3 months, you need another shot. However, the effects (not the protection) may linger longer, up to 10 months after the last shot and during that time it may be harder to get pregnant. But eventually the effects wear off.
I have heard that it can stay in your system for 30 days but that does not affect the outcome of a drug test. You should call your Dr's office and get all the details.