The 21-year-old, who has made 44 appearances for Leeds during his breakthrough season, suffered another break during the weekend draw at Cardiff.
"It was pretty sore and numb afterwards and I couldn't feel it," Lees told the club's website. "But I'm getting used to it now.
"It was the fourth time I've done it since January now so it's broken and needs putting back in place. I've been waiting to get it done so it will wait until after the season."
Lees was first to admit his latest injury paled into insignificance compared to team-mate Leigh Bromby, who will be sidelined for up to a year after rupturing his patella tendon in the same match.
"It was pretty sickening to see on the pitch," Lees added. "We were all just devastated for him because he's had a few niggles this season and has worked so hard to get fit."