No charges have been filed against Smith, who has been released on bail, district attorney's office spokeswoman Shiara Davila-Morales said.
Smith, 24, posted $20,000 bail hours after he was arrested on suspicion of falsely reporting he had a bomb to a Transportation Security Administration agent at LAX.
Los Angeles airport police Sgt. Karla Ortiz said that police had not verified whether Smith was intoxicated during the incident. Since officers were responding to a report of him making a false report of a bomb, they were not required to test him for drugs or alcohol.
At about 2 p.m. Sunday, Smith, listed by airport police as a San Jose resident, was going through security screening in LAX's Terminal 1 and was "randomly selected for a secondary screening," Ortiz said in a statement.
"The suspect then became belligerent and uncooperative with the process with the TSA agent, making a comment indicating that he was in possession of a bomb before proceeding towards the gate area," Ortiz said.
"Los Angeles Airport Police made contact with him at the gate and he was positively identified as the person in question," Ortiz said. "Once again the male subject became uncooperative and he was detained and taken into custody by Airport Police."
Smith was transported to the Los Angeles Police Department's Pacific Division, where he was booked at 4:16 p.m. and was released from custody after bailing out at 7:02 p.m., according the sheriff's department jail records.
49ers general manager Trent Baalke said in a statement, "We are disappointed to learn of the incident involving Aldon Smith. As this is a pending legal matter and we are still gathering the pertinent facts, we will have no further comment."
Sunday's arrest is the latest legal woe for the 49ers' star linebacker, who has 42 sacks since being drafted in 2011.
The Santa Clara County District Attorney's Office has charged Smith with two misdemeanor counts of DUI after he crashed his car into a tree in San Jose last Sept. 20.
Prosecutors also charged him last October with three felony counts of possessing an illegal assault weapon after sheriff's deputies found three assault rifles in his San Jose home in 2012.
Both cases are pending in Santa Clara County Superior Court in San Jose.
Smith also spent several weeks in a rehabilitation facility for alcohol abuse in 2013.