Hamilton County Chief Deputy Prosecutor Andre Miksha said prosecutors are not bound by preliminary booking charges.
Prosecutors and Irsay's family have said he is undergoing treatment at a facility outside of Indiana.
Irsay, 54, was arrested near his home in suburban Carmel after he was spotted driving slowly, stopping in the roadway and failing to use a turn signal. Police said Irsay failed several roadside field sobriety tests before he was arrested.
Police said they found multiple prescription drugs in his vehicle. The drugs were not associated with any of the pill bottles found inside, and police said some were not in bottles.
Authorities would not say what drugs Irsay was allegedly caught with, but they were listed as Schedule IV drugs by the Drug Enforcement Administration. That type of drug, which includes Xanax, Darvocet and Ambien, has a low risk for abuse or dependency, according to the DEA.
An NFL spokesman has said Irsay is subject to discipline, but did not elaborate.
Irsay acknowledged in 2002 that he had become dependent on painkillers after several years of orthopedic operations but said he had overcome the problem after undergoing treatment.
Irsay became the Colts owner in 1997 after the death of his father, Robert Irsay, and a lengthy legal battle with his father's second wife. Forbes magazine has estimated Irsay's net worth at $1.6 billion.
Irsay made headlines in 2001 by buying the handwritten scroll manuscript of Jack Kerouac's beat poem "On the Road" for $2.43 million and sending it on a nationwide tour.