According to a Utah news release, Falemaka, 20, and Brooks-Brown, 18, are expected to recover. Both were shot in the torso.
"Obviously, our first concern is that both Lo and Marcel are going to be OK, which appears to be the case," Utah coach Kyle Whittingham said Sunday in a statement. "We don't have all of the details yet, but it is our understanding that they are the victims in this incident and we feel very fortunate that they are expected to fully recover.
"It is unknown at this time how soon they will be able to return to the football field, but we are optimistic it will be in the near future."
According to police reports, the shooting happened at 11:53 p.m. Saturday at a private party when three men, who are described as the suspects, refused to leave, Salt Lake City police spokeswoman Robin Heiden told The Associated Press. One of the suspects pulled out a gun and shot the players.
Police are looking for the three suspects.
Falemaka, who grew up in West Valley City, Utah, started as a walk-on in 2013. He is on scholarship. The tight end has appeared in two games this season on special teams.
Brooks-Brown, of Rio Linda, California, is in his first season and was expecting to redshirt.
Information from The Associated Press was included in this report.