Coach Andy Reid said Moeaki was undergoing further examinations before Monday's practice and did not indicate how long the fourth-year pro would be out.
Turns out that general manager John Dorsey and Reid knew what they were doing.
The Chiefs play their final preseason game Thursday night against Green Bay, and final roster cuts are due Saturday. Moeaki is not signed by Kansas City beyond this season.
Bears running back Michael Bush recently told the Chicago Tribune that he played most of last season with a fractured bone in his right shoulder, so it's not a foregone conclusion that Moeaki will end up on injured reserve -- or even miss a significant amount of time.
Moeaki dealt with a series of injuries during his college career at Iowa, but he seemed to have put them behind him after the Chiefs drafted him in the third round in 2010. He played in 15 games and caught 47 passes for 566 yards and three touchdowns.
Then came the 2011 season, when Moeaki tore his left ACL in a preseason game against the Packers. He had surgery to repair the damage and missed the season.
Moeaki battled a series of injuries again last season, including a head injury that kept him off the practice field late in the year. He suited up for 15 games but had just 33 catches for 453 yards and a touchdown during the Chiefs' 2-14 season.
"He's had a couple of injuries, but I think some of those -- in a lot of cases, with different players, sometimes you can change that around in your career," Reid said. "Hopefully this is his last one and he'll be able to keep going."
The Chiefs were already banged up at tight end with Kelce dealing with a bruised knee that kept him out of the Steelers game. Reid said Kelce could be back in practice this week.
Reid indicated during training camp that the Chiefs would rely heavily on their tight ends, even putting three on the field at one time. Fasano has been getting the most reps with the first-team offense, while Kelce had moved ahead of Moeaki on the depth chart.
"I'm not sure exactly what injury Tony has right now," Fasano said, "but if we were to lose him for any amount of time, it'd be a loss. We did a good job in camp defining our roles as the tight end position is concerned in our offense, and we were really going to complement each other well, but hopefully it's not as major as people are making it out to be."
Kelce is less polished in the blocking game, but the former Cincinnati standout has been praised for his speed and ability to stretch the field.
"Travis has come a long way even from spring," Fasano said. "For a rookie, he has a lot of confidence and a great skill set. Losing Tony, if that were to happen, would definitely be a loss, but I think our tight end position would be able to step in and fill the void."