Williams, who turned 19 in April, was arrested on suspicion of underage drinking in February, but in March, when the charges became public, coach Bronco Mendenhall said the issue had been dealt with internally and Williams was in good standing with the university and the program.
BYU's honor code forbids the use of alcohol and illicit drugs.
Williams said he is being punished because of a "combination" of that incident and something that happened in July. He declined to confirm whether the second incident was alcohol-related, saying that he was "just having fun. … It was back home stuff. It was just my choices, but it isn't happening any more."
Rumors have flown on BYU message boards and Twitter since a July 11 party in Provo that suspensions for violating the honor code were coming for a handful of football players, but Williams was the only player on Friday to acknowledge he has been punished.
Mendenhall wouldn't confirm or deny that more players have been suspended and said there won't be any announcements from him as camp unfolds.
"Any other players that need development, I will handle internally, and I will act appropriately," Mendenhall said. "Any other issues that we have, not only now but in the past, I know will be for the player's benefit. I am anxious to move forward."
Mendenhall said Williams' announcement "kind of put me on reaction mode" and said he didn't instruct the junior to talk about, or not talk about, the suspension.
Asked if he expects to have his full complement of defensive backs available for the opener, defensive coordinator Nick Howell nodded affirmatively and said, "I am planning on it."
But when asked if other players besides Williams would be suspended, he said he wasn't sure and that it was a question for Mendenhall to answer.
Generally, coaches and players described the first day as typical, and Mendenhall said his main takeaway was that the Cougars have increased their speed and athleticism on the perimeter and that the defensive linemen are better prepared for the season than he thought they were going to be.
Quarterback Taysom Hill threw a 55-yard touchdown strike to junior college transfer Nick Kurtz, and looked sharp on almost all his throws. Hill said the team "fully supports" Williams and will rally around him as he struggles through his suspension.
Hill said there is no dark cloud hanging over the squad as it deals with Williams' suspension and the possibility of more.
"I think that just goes to show what type of kid Jamaal is," Hill said. "He has had a little bit of difficulty, but he has handled it really well. It could be a distraction, and he could feel bad for himself, all those things. But he has come out and helped the young guys learn that position."
The Cougars said hello to a new player, University of Utah transfer and returned missionary Harvey Langi, who will wear No. 21 and play linebacker at his own request, Mendenhall said. They said goodbye to three players who are giving up football for medical reasons: receiver Brett Thompson, defensive end Kevan Bills and safety Drew Reilly.
BYU camp Day 1 storylines
O Running back Jamaal Williams confirms that he's suspended for one game due to honor code violations and will miss the opener at Connecticut.
• Coach Bronco Mendenhall said WR Brett Thompson, DE Kevan Bills and DB Drew Reilly are retiring from football due to medical reasons.
• Deep snapper Kevin O'Mary was granted an additional year by the NCAA and will serve in that position again this year.