Milner-Skudder broke bones in his foot while playing for the Wellington Hurricanes against the Waikato Chiefs on March 10 and was expected to be out of action for six weeks, but Boyd said on Saturday the injury was taking longer than expected to heal.
"The solidification of the bone in his foot is slow," Boyd told New Zealand radio station Newstalk ZB on Saturday. "It's a low blood-flow area, so it's slow.
"We initially thought six weeks, so post the bye that's coming up after Blues and Brumbies.
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"He may be ready to come in at the back end of that, he may not."
The 26-year-old scored a try in the World Cup final in 2015 and was then named World Rugby's Breakthrough Player of the Year but has been blighted by injury since and missed virtually all of 2016 as he recovered from shoulder surgery.
Boyd said Milner-Skudder had been working hard to do all he could to get fit in time for the visit of Warren Gatland's Lions, with the first match of their tour on June 3.
"He's worked incredibly hard to keep fit and strong and healthy in other ways, but he's got a wound that's not helping him at the moment," Boyd added.
"I don't think he would have played an awful amount of rugby, before they pick the All Blacks.
"Whether that's the preparation that the All Blacks want for that, it depends what sort of back three they're looking for and who else is fit.
"I think (he) will be available, but he won't have played a whole lot of rugby."
The Hurricanes play the Blues at Eden Park later on Saturday and then meet the ACT Brumbies in Napier next week before they have their second bye of the competition.
(Reporting by Greg Stutchbury; Editing by Peter Rutherford)
