Ray did not practice in the team's organized team activities Monday and it is possible he could miss next week's three-day minicamp.
"Shane's got a little wrist [injury] going on right now, so we're not sure," Joseph said. "We're taking it slow, just being smart with guys. It's the spring. Our real goal is to get him healthy for training camp, but right now we're being smart with Shane."
Joseph also added Ray's current injury is related to the wrist injury he sustained last season.
Last month, Joseph said he believed Ray received a wakeup call when the Broncos elected against picking up his fifth-year option.
Had the Broncos picked up his option, Ray would have received a salary of $9.232 million guaranteed against injury only in 2019.
Ray has recorded 84 tackles and 13 sacks in 38 career games since being selected with the 23rd overall pick of the 2015 NFL Draft out of Missouri.
However, the 25-year-old had only one sack last season as he battled a wrist injury and played in only eight games.
Ray finds himself behind All-Pro Von Miller and the promising Shaq Barrett. The Broncos also used the fifth overall pick of the 2018 NFL Draft last week to select pass-rushing specialist Bradley Chubb of North Carolina State.