Does vaginosis antibiotic causes dark brown urine?

Yes it can. You are probably taking Flagyl (metronidazole) for bacterial vaginosis. Flagyl can cause a darkening of urine. This is generally a harmless effect when taking the medication.
No. Either the person taking the antibiotic for vaginosis is not drinking enough fluids, resulting in concentrated urine or else, there is something else going on. I highly recommend that this person see a healthcare professional today, to determine the cause of the dark brown urine, and to rule out any serious kidney conditions.