Joe Simpson -- Jessica Simpson's father -- was arrested for DUI in L.A. ... TMZ has learned.
According to law enforcement sources, 54-year-old Joe was busted on Ventura Blvd. in Sherman Oaks on August 4.
We're told LAPD cops pulled Joe's car over around 10 PM ... and during the stop, officers got the feeling he was intoxicated and ultimately cuffed the famous pop and took him to the pokey.
Joe was booked and spent the rest of the night behind bars. He was released without having to post bail at 9:41 the following day.
The case has not been sent over to prosecutors in the L.A. City Attorney's Office yet, but if criminal charges are filed, it's likely Joe will not get any jail time since it's his first offense. He'll probably end up with a big fat fine -- something his daughter will have no problem paying.