Hurd has been dealing with back problems that kept him out of the 49ers' final two preseason games.
"It's a little more serious than we thought," Shanahan told reporters after the 49ers' preseason finale loss to the Los Angeles Chargers. "Still don't know for sure. We thought we would have a better chance at (him playing in) Tampa, but now that's not looking as good."
Shanahan went on to say that Hurd isn't likely to be in danger of landing on an injury list, just that his availability for Week 1 is more uncertain than previously believed.
"It's just we're not as confident that he'll be available Week 1, now," Shanahan added. "Still, we aren't for sure, but I was a lot more optimistic about that two days ago."
The 49ers made Hurd a third-round pick out of Baylor in April. He had three catches for 31 yards with two touchdowns in San Francisco's preseason opener against the Dallas Cowboys but was held without a catch in the next game against the Denver Broncos.
Hurd did not play against the Kansas City Chiefs or Chargers.