The news comes a season after quarterback Everett Golson was suspended for the 2013 season for academic impropriety and after Daniels was suspended for the spring semester.
The Irish finished 9-4 behind Tommy Rees last season, but coming off an appearance in the BCS title game in 2012 it was a step back.
Golson has returned, but now coach Brian Kelly could be scrambling to fill holes before opening his fifth season in South Bend at home against Rice on Aug. 30.
Athletic director Jack Swarbrick said Kelly was "devastated" by the news.
Jenkins and Swarbrick expressed support for Kelly.
"We have great confidence in Brian and his staff," Jenkins said. "They have been nothing but supportive."
Jenkins said the investigation shows Notre Dame's honor system works, saying it was started when someone on the university staff became suspicious of papers and homework turned in by the players.
"At any university you're dealing with young people. The vast majority of them make good decisions. But young people sometimes make bad decisions," he said. "Our job is to hold them accountable and to use those incidents as ways to educate them. That's what we're doing."
Jenkins said Notre Dame has notified the NCAA about the inquiry. Because of potential violations, the four players can't compete until the conclusion of the investigation and the university honor code process.
Jenkins said during a news conference that no student has been judged responsible for "academic dishonesty."
"Nobody has been dismissed," Jenkins said.
Jenkins said there is no timetable regarding how long the investigation will take.
"We will take as long as it takes to have a thorough and fair investigation and proceed through our academic honor code process," Jenkins said.
He added that such investigations at Notre Dame aren't common "but it happens."
The university also is investigating if other students are involved. Jenkins said it was too early to say if the four players acted together.
Jenkins said if it is found they violated the school's honor code the penalties could range from an F on an assignment, to an F in the course, to dismissal from school. The penalty would be decided by an honor committee.
Swarbrick said the players haven't been suspended. He said they remain grant-in-aid students and have access to athletic facilities and resources.
Jenkins said he didn't want to speculate on possible NCAA punishment, while Swarbrick said the NCAA usually defers to a university when it comes to academic integrity.
"There are a few narrow instances where that triggers an NCAA concern, but I must stress we have no evidence of most of those here. No involvement by a member of the coaching staff, no transcript impropriety, those sorts of things," he said. "If it has NCAA consequences, we'll let them know."
Jenkins said the school would vacate victories if it is determined players have been ineligible during past competition. All four were members of the 2012 team that played for the BCS national championship.
The investigation is the latest in a series for the Irish in the past 15 months involving academics, starting with Golson.
Jerian Grant, the leading scorer on the basketball team at the time, was suspended in December for the spring semester because of an academic violation. Daniels was suspended two weeks later for the spring semester and was recently reinstated.
Swarbrick said the previous cases were different.
"Let's not confuse academic probation, where you don't make grades in a semester, with academic dishonesty. They are very different things," he said.
Jenkins said he doesn't believe it's a sign Notre Dame has to make changes in the student-athletes it admits.
"We're confident that the students we admit have the capacity to be successful," he said.