Wilson, a sophomore, suffered a head injury against Arizona State on Nov. 9 and started having headaches the next day.
Wilson will at least miss the rest of the season, the school said Monday night.
"A preexisting condition was discovered after Travis Wilson underwent a CT scan to further evaluate the symptoms of a concussion," Utah team doctor David Petron said in a statement. "The findings on the CT scan led to an evaluation with an angiogram, which showed what appears to be a previous injury to an intracranial artery.
"We do not believe it is life threatening and there is a possibility he could play football in the future if it remains stable. It will be further evaluated with follow-up testing in approximately three months."
Before the statement was released, Utah coach Kyle Whittingham did not discuss the specifics of the injury.
"I'm not a doctor and wouldn't want to screw up [the specifics of the injury]," Whittingham said. "It's pre-existing. I'm not even sure it's head trauma. It could be genetic. I'm not completely involved in that part of it.
"The way I understand it, this is not a life-threatening condition, but it may put him at higher risk because of it if he were to continue to play. But that is still to be determined."
Wilson was not diagnosed with a concussion during or after the game, and Whittingham said the injury suffered against ASU is not related to what they found during the angiogram.
"Travis is done for the season," Whittingham said Monday. "He has been declared unable to play for the rest of the year. It could be career-ending. We'll find out. We won't know for certain for several months.
"Travis is a tough, competitive kid, and very upset by this, obviously. Disappointed. ... The most important thing is his long-term health, and that's all that anyone is concerned with right now. That is the bottom line. The medical staff is proceeding to make sure that everything is done in the proper way to make sure that is the thing that we're addressing."
Wilson did not travel with the Utes (4-6, 1-6 Pac-12 South) during their 44-21 loss to Oregon on Saturday.
Utah visits Washington State on Saturday before closing out the season at home against Colorado on Nov. 30.
Wilson ends the year with 1,827 yards, 16 touchdowns and 16 interceptions and a 56.1 completion percentage. He also rushed for five touchdowns.
"We want Travis around the program and close to the program," Whittingham said. "Travis will address the team [Monday]. He wants to do that. As far as we're concerned, he's a part of our team."
Adam Schulz, who started against Oregon, will close the year as Utah's starter. He was 13 of 30 for 181 yards with a touchdown and an interception in the loss to the Ducks, and he also rushed for a score.
For the season, Schulz is 35-of-75 with two touchdowns and two interceptions.
Freshman Connor Manning, who is redshirting, will move to No. 2 on the depth chart. Whittingham said Manning will not see playing time, however, unless an emergency arises.
Wilson's teammates want him to know they will be there to support him.
"The team is just going to really come around him and help him out in this situation,'' Utah tight end Jake Murphy said. "Despite what people think, football isn't life."
Information from The Associated Press was used in this report.