X-rays reportedly were negative for the 27-year-old Vernon, who was carted off the field after his foot was tangled with an offensive lineman during a drill.
NFL Network's Ian Rapoport reported that Vernon is also dealing with a deep bruise on his ankle that will keep him off his feet and clouds his timetable for return.
"Yeah, you don't want anybody getting hurt," Giants head coach Pat Shurmur said following practice. "You want guys to be able to practice and stay healthy. We'll just see."
Vernon recorded 6.5 sacks in an injury-filled season last year for the Giants, who open the season against the visiting Jacksonville Jaguars on Sept. 9.
The 6-foot-2, 270-pound Vernon will be shifted to outside linebacker in the team's 3-4 scheme to maximize his pass-rushing skills.
Vernon started all 16 games and registered 8.5 sacks in 2016 after signing a five-year, $85 million contract that included $52.5 million in guaranteed money.
A third-round pick of Miami in the 2012 NFL Draft, Vernon notched 29 sacks in four seasons with the Dolphins, including a career-high 11.5 in 2013.