Kennedy, who is one of the leading chances to win the Brownlow Medal, came off the ground early in the second quarter of last Saturday's home win over St Kilda.
The star midfielder has escaped a tear, but coach John Longmire indicated on Monday Kennedy was unlikely to be risked in Sunday's match against Western Bulldogs at Etihad Stadium.
"His hamstring is tight, he's got a little bit of fluid on the outside of his hamstring but there's no tear in there, so that's a really good sign," Longmire said.
"It would be fair to say we're not going to put him at risk this week.
"If he's not any good at the back end of the week, he won't play.
"If he doesn't play this week, it will only be one week."
Longmire said another midfielder, Craig Bird, was also unlikely to miss more than one game after suffering a posterior cruciate ligament knee injury on Saturday.
He said key forward Sam Reid was still a little bit sore from the weekend and would be monitored during the week, but midfielder Dan Hannebery was OK after suffering a minor knock against the Saints.
Longmire said Ben McGlynn was likely to be out for one more week with his calf strain but said defenders Nick Smith and Rhyce Shaw were each a big chance to return this weekend and would be the logical replacements for Kennedy and Bird.
