ESPN's Mike Reiss reported Thursday the injury, which has caused Harris to miss the last two days of practice, could ultimately "threaten his availability for the season opener" on Sept. 13.
He underwent surgery on his pinky finger, which will require a "few weeks to heal," per Ian Rapoport of the NFL Network.
The 23-year-old University of Alabama product had a limited impact as a rookie after the Pats selected him in the third round of the 2019 NFL draft. He made just two appearances, rushing for 12 yards on four carries while buried on the team's depth chart.
Harris had made a strong case throughout training camp to earn a more extensive role in 2020, and Patriots head coach Bill Belichick took notice last month.
"He's a smart player, and he has a lot of skills that I think we'll be able to utilize," Belichick told reporters. "He's had an opportunity to get quite a few reps here in the work that we've done to this point, so I think that's helped him, but he seems like he's in good shape and ready to go. Looking forward to seeing him."
Now, after working his way into first-team reps, he could risk sliding back down the depth chart by the time he's cleared to return.
Sony Michel is back after missing the opening stages of camp with a foot injury, and the Pats also activated Lamar Miller from the PUP list as he completes his recovery from a torn ACL that caused him to miss the entire 2019 season with the Houston Texans.
That duo is joined by James White, Rex Burkhead and undrafted rookie J.J. Taylor in the fight for roster spots and involvement in the Week 1 game plan.
Harris should be far more involved during his second NFL season, but the injury is a setback just as the hype train was starting to pick up steam thanks to his strong camp.
If he misses the Week 1 clash with the Dolphins, his next chance to play would come Sept. 20 when the Patriots travel to CenturyLink Field for a Sunday Night Football meeting with the Seattle Seahawks.