Timlin suffered the injury on a comebacker in a Triple-A game.
The setup man had to get two stitches in the finger.
"I don't know yet," Timlin said of being ready for the opener. "We have to check it out. I can play catch. The ball hit me off the end of the finger. I tried to get my hand out of the way, actually. I wasn't trying to reach and catch the ball."
The Red Sox must set their 25-man roster before the opener against Oakland.
"His availability is certainly in question," said Francona.
The good news is that center fielder Coco Crisp is probable, as he just recently started playing in games after being sidelined with a groin injury.
If Crisp isn't activated for the two regular season games in Tokyo, Francona is confident he'll be ready by the time the Sox resume their schedule in Oakland on April 1.
At this point, rust is more of an issue for Crisp than health. Even if he can serve as a pinch-runner or defensive replacement, the Sox will probably activate him for the games in Tokyo.
Ian Browne is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.