"I wasn't ready today," Kinsler said on Friday. "It's getting close."
Tigers manager Brad Ausmus said Kinsler could possibly be rested until the team's next series, which begins on Tuesday in Arizona.
"He still feels it a little bit," Ausmus said, "so we're just going to kind of go day to day, and if need be we'll go through the off-day."
A trip to the 10-day disabled list would keep Kinsler out until May 14.
Utility man Andrew Romine, who took over for Kinsler on Wednesday, assumed second-base and leadoff duties for the Tigers on Friday. Romine entered Friday's contest with a .254/.302/.390 slash line, one homer and six RBIs in 59 at-bats this year.
"It's just something that I want to be sure I'll be ready to go," Kinsler said. "No reason to push it and make it get worse."
The setback comes at a time when Kinsler has been struggling at the plate. Over his past eight contests, Kinsler is batting .094 (3-for-32) with four runs scored, three walks and three strikeouts, dropping his average from .262 to .206 in that span.
• Ausmus said the Tigers will take a patient approach with slugging right fielder J.D. Martinez, who has been on the DL since the start of the season because of a ligament sprain in his right foot. Martinez went 2-for-4 with a double and a run scored for Class A Advanced Lakeland on Friday, and he is scheduled to play five to seven innings in the field on Saturday.
"I can't give you a time frame," Ausmus said of a possible return date. "It's all on J.D. and how he feels. He's going to let us know when he thinks he can play. … The most important thing is he's going to have to play the outfield. If he's going to come up here he's going to have to play the outfield."
• Outfielder JaCoby Jones (lacerated lip) continued his rehab assignment for Triple-A Toledo on Friday. Ausmus said the organization wants to give him more at-bats and "get him in a groove" before reinstating him from the disabled list. Meanwhile, Jim Adduci has capitalized on his promotion in Jones' absence, batting .323/.364/.484 in nine contests.
"It complicates things," Ausmus said of Adduci's production. "He's been swinging the bat very well and I hope he continues to make it a more complicated and a more difficult decision."