Hinrich will see a doctor on Monday.
"Its still really sore," said Hinrich, who was struggling just trying to tie his shoes. "It doesn't feel strong. I have trouble gripping.
"I'm supposed to see a doctor [on Monday]. I'm pretty confident [my absence is] not going to be long, and hopefully make some progress here in the next couple days and get back out there."
Hinrich injured the thumb during practice Wednesday and missed Thursday's game against Utah. While he wouldn't completely rule out playing against the Bucks, he made the possibility seem like a long shot
"I'd have to improve considerably from today to [Monday]," he said.
Hinrich missed most of last year when he tore ligaments in his right thumb, and he admitted that he initially thought he might have suffered the same injury to his left thumb.
"I was worried about it," he said. "Just the fact last year ... I felt like I just jacked up my thumb. It didn't feel like anything real serious.
"So I was nervous going into the MRI [on Friday], but very excited to get the good news and hopefully be back as soon as I can."
Bulls coach Vinny Del Negro is hoping the hand specialist delivers good news on Monday.
"With Tyrus [Thomas] out and Kirk out, it's 20-plus points out of the lineup, and leadership and defense and shot-blocking and things that we desperately need," Del Negro said. "But, we can't control the injuries, and we need to get those guys back healthy and as quick as possible. But, I'd hate to rush something.
"But, if the doctor says his fingers very stable and Kirk feels like he can contribute, he'll be out there. Kirk's a tough guy, he's a competitor. When he's ready, he'll be out there."
Nick Friedell covers the Bulls for ESPNChicago.com.