The 24-year-old, who signed a new deal in November, has had an impressive season as part of Wolves’ solid back three.
However, he landed awkwardly on his ankle during Wolves’ open training session last week and gingerly hobbled off the field – missing the subsequent game away at Burnley.
Now, head coach Bruno Lage believes it is unlikely Kilman will play in any of Wolves’ remaining five fixtures as they work to assess the damage caused.
“With Max, to be honest it will be hard for him to return,” Lage said.
“We have 25 days in front of us and I don’t believe he will recover.
“The doctors are doing a fantastic job and sometimes we recover players after time, so let’s see what can happen with Max. He twisted his ankle and we need to understand what is the problem.”
Despite a largely positive campaign so far, Wolves have also been blighted by injuries.
Lage has spoken publicly about his desire for a larger squad and two competitive players for each position and following Kilman’s knock the manager again stressed the need to make additions for next season.
“This is football and that’s why I said many times that I don’t believe in luck,” he added.
“I believe in hard work to plan the best squad because we know these kind of things happen and we need to have the solutions for when these kind of things happen.”