Los Angeles District Attorney's spokeswoman Jane Robison says Ghalib was taken into custody immediately after being sentenced Friday.
He pleaded no contest last month to leaving the scene of an accident that injured a man who was trying to serve him with a restraining order. The order was sought by Spears' father and was eventually granted.
The process server has sued Ghalib, a paparazzo. That case is still pending.
Robison says Ghalib was also ordered to serve three years of formal probation and perform 45 days of roadside cleanup duty.
The 37-year-old was facing up to a year in county jail.
