St. Landry Parish Sheriff Bobby Guidroz said Thursday night that 33-year-old Brandon Scott Lavergne was booked on first-degree murder and aggravated kidnapping charges by police in Lafayette, where Shunick went missing May 19.
Guidroz said the arrest came as his department helped Lafayette police search Lavergne's residence for evidence. The search continued Thursday night.
The sheriff gave no details about what was found. Lafayette police also released no details. Police have scheduled a 1 p.m. Friday news conference to discuss an arrest in the case.
It was not immediately clear if Lavergne has an attorney.
The rural St. Landry address where the search was conducted is listed as the address of Lavergne on the state's sex offender website.
The website says Lavergne was convicted in 2000 of aggravated oral sexual battery. He was released in 2008.
Shunick was last seen shortly before 2 a.m. on May 19, days before her 22nd birthday. The University of Louisiana at Lafayette student had left a friend's house to ride her bicycle home.
Her bicycle was found eight days later in a remote, swampy area under a highway bridge in Iberville Parish, about 25 miles from the spot where she was last seen.
Soon after her disappearance, Lafayette police released video taken about the time she went missing. It showed her cycling on a Lafayette street around 1:45 a.m. on May 19. Investigators said at the time that they were seeking information about a pickup truck seen on the video. The sex offender website shows a white 2011 Chevrolet Silverado under vehicles linked to Lavergne.