The 32-year-old right-hander won't be on the active roster for Monday's opener against Minnesota because of tightness in his right triceps.
"I think they used the word strain," Verlander said. "It felt like just a little cramp but, obviously, with it taking a little longer to heal, it's probably a little bit more than that — just take it day by day."
Verlander has been throwing lightly in an attempt to work out the tightness.
"I don't think this is going to be a long-term issue," Tigers Manager Brad Ausmus said. "After throwing yesterday, he said he felt as good or better today."
Detroit will make his DL stint retroactive, making it possible the six-time All-Star could start the sixth game of the season, on April 12 at Cleveland.
The 27-year-old Cahill was 3-12 with a 5.61 ERA for Arizona last season. The right-hander was an All-Star with Oakland in 2010. Cahill is 64-69 with a 4.07 ERA in six seasons.
The 24-year-old Elander is a .275 hitter in three seasons in the minors.