Packers head coach Mike McCarthy told Demovsky:
"He's going to be a couple of weeks. They were encouraged once they got all the testing done."
Bostick was hurt three plays into his team's 21-7 win over the St. Louis Rams Saturday when he caught a pass. Bostick was expected to compete with 2014 third-round draft pick Richard Rodgers for the starting tight end spot in the absence of Jermichael Finley, who is currently a free agent after sustaining a spinal injury last season.
The Packers play in the earliest game of the NFL regular season on Thursday, Sept. 4, when they face the Super Bowl-champion Seattle Seahawks at CenturyLink Field.
Bostick played in 11 games in the 2013 season, catching seven passes for 120 yards and one touchdown.
- Will Green