The Twins transferred Kirilloff (back) from the 10-day injured list to the 60-day IL on Tuesday.
The 26-year-old now won't be eligible to be reinstated until mid-August, but he wasn't likely to return within the next couple weeks regardless given the lack of recent updates in his rehab program. If not for the back strain, Kirilloff was set to be demoted to Triple-A St. Paul due to his .654 OPS this season, so the Twins will likely send him on a lengthy rehab assignment once he's game ready in an attempt to get him back on track.