Teixeira was scheduled to receive a platelet-rich plasma shot on Monday from Yankees team physician Christopher Ahmad.
"You really don't know exactly how it's going to respond," Teixeira said. "So that's why we say we'll re-evaluate in three to four days, and hopefully the back responds really well to the PRP. If that happens, then hopefully I'll be back soon. If not, it might take a few more days after that."
Teixeira has hits in just three of his last 24 at-bats and said the All-Star break may have contributed to his increase in pain.
"That's kind of what happens when you shut down for a little while," Teixeira said. "The blood's not flowing, you don't have that adrenaline pumping through your body and it becomes worse. I think that's what we saw this weekend."
In place of Teixeira for Monday's series opener against the Rangers, Kelly Johnson started at first base and batted fifth. Johnson and Brian McCann took grounders at first base during batting practice.
The Yankees believe that Teixeira's strain is mild and won't force him to the disabled list.
"We're really hoping it won't," manager Joe Girardi said. "I think if we were really concerned, we'd put him on the DL right away. We're hoping that after three to four days, maybe he feels OK and maybe we'll get him back in there."
A right wrist injury limited Teixeira to just 15 games in 2013, but this year, he has dealt with a variety of nagging injuries. Before this issue, the 34-year-old Teixeira had missed time this year with right wrist inflammation, a right hamstring strain and knee problems.
"It's tough," Teixeira said. "I thought the year off last year would give me a fountain of youth, and it's just made me rusty. Really, I've used that word a few times this year. It's been something every game."
Teixeira has played well when in the Yankees lineup -- entering Monday, his 17 home runs and 48 RBIs led the team.
"I'm still happy with the way I've played when I'm healthy," Teixeira said. "I just need to get healthy again."