"Words cannot express the disappointment we feel knowing that one of our players was arrested as a result of this investigation," the team said in a statement.
The NFL released its own statement, calling the involvement of a player in the case "deeply troubling."
Both the NFL and Patriots expressed sympathy for the victim's family.
On Wednesday, about a half-dozen plainclothes police officers went to Hernandez's house and then led him out in handcuffs. He was wearing a white T-shirt and shorts.
Sheriff: Gang unit will investigate Hernandez's tattoos
Bristol County Sheriff Tom Hodgson said he expects living behind bars will be a major adjustment for the former NFL star.
Wednesday night's dinner at the Dartmouth House of Correction was chop suey, green beans and a slice of bread, the sheriff said. Hernandez will only be allowed out of his one-person cell for showers and phone calls. Authorities will perform background checks on any visitors.
Hodgson said he met with Hernandez "as soon as he came in" to the facility and told him he'd receive no special treatment.
Asked how Hernandez responded, Hodgson said, "He did not seem nervous," adding he was "polite and respectful."
Hernandez is currently being held in the jail's medical unit while he undergoes further screening, including mental health, physical and security tests.
As part of the security screening, authorities will determine whether he has any gang affiliations.
"He had tattoos that our gang unit would be looking at ... to see if he's involved in any kind of gang," Hodgson said. "Doesn't mean he is."
The tattoos raise suspicion, the sheriff said, and investigators will follow up with interviews to further determine the significance of what they saw.
"He'll be treated no better and no worse than any other inmate," the sheriff said.