The latest injury occurred during practice on Monday, when rookie point guard Tyler Ennis hit Len's hand as Len went up for a dunk.
"As soon as I landed, I thought it was the same finger," Len said. "It was still sore from before because it wasn't healed all the way yet.
"It's just a pinkie. I don't get discouraged. Everything is going to be all right. I can still work on a lot of other things. I can run and do conditioning stuff, work on my left hand, pass the ball, even can guard or do so something. It's just a pinkie. It's nothing major. It's nothing compared to ankles."
Len, 21, was limited to 42 appearances and 8.6 minutes per game during his rookie season in large part because he was working his way back from surgeries on each ankle. The Suns' No. 5 overall draft pick is being counted on this season to provide more minutes at backup center. Last season, Suns coach Jeff Hornacek often rotated Miles Plumlee, Channing Frye and Markieff Morris at the two big man spots because of Frye's versatility to man both positions.
"I think he'll be out maybe a week, week and a half from the contact," Hornacek said of Len. "But then they'll tape it up and he can go."