Alonso was scheduled to have a cortisone shot in the hand later Tuesday, but at this point he's been told the only thing he can do for the hand is rest it.
"We're working through a couple of scenarios where we'll give it rest with the hope that I will be able to come back sooner than later," he said.
The good news was that no surgery is expected on the hand, which caused him to miss 34 games earlier this season. He said that even after returning from the disabled list, the strength in his hand wasn't the same as it was earlier in the season.
The initial diagnosis was that Alonso would miss between seven and 10 days, but it now appears that he will miss more time than that.
"He could be back in a couple of weeks," said Padres manager Bud Black. "He wants to get back and play again, which is great."
Alonso said there's no sense in him rushing back, especially since there's just 24 games remaining in the regular season after Tuesday.
"I'm not even 90 percent now, so what's the point in coming back before I'm healthy?" he said.
Alonso said his hand hasn't felt fully healthy since before his previous injury. He hit .284 with six home runs, 29 RBIs and seven doubles in 190 at-bats before that first injury. Since then, he's hitting .278 with four doubles and 16 RBIs.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter. This story was not subject to the approval of Major League Baseball or its clubs.