The German is Lazio's top-scoring striker this season with seven goals in the league, but he may have played his last game of the season after suffering the injury.
Klose's last appearance for Lazio came in their 3-2 victory over Parma at the end of March. He was not involved in their win over Sampdoria last weekend and the club have confirmed a hamstring problem has been identified.
Uruguayan midfielder Alvaro Gonzalez is also set for a spell on the sidelines with a muscle injury, and he too is expected to be out for at least a month.
"Today Miroslav Klose and Alvaro Gonzalez were subject to specialist investigations," the club announced on their website.
"Investigations on Klose showed the presence of a lesion on his left hamstring, (with) the expected recovery time four weeks.
"Alvaro Gonzalez (also) showed the presence of a lesion on his right thigh."
Lazio, who can still qualify for Europe next season, have six games remaining of the league campaign including matches against Napoli and Inter.
