The Argentinian scored twice in Inter's 2-0 Serie A victory at Sampdoria on Wednesday night to bring his personal tally up to 18 goals, meaning his absence for the season run-in could prove crucial to Inter's chances of securing Champions League football for next season.
A statement published on Inter's official website read: "Rodrigo Palacio has undergone medical examinations which have revealed a muscular problem to the back of his left thigh."
Club doctors will conduct further tests on the former Genoa player this evening to confirm the extent of the injury and establish a likely prognosis for his recovery.
The 31-year-old joins countryman Diego Milito, who will miss the rest of the season with a leg injury, on the sidelines, leaving Tommaso Rocchi and Antonio Cassano as the club's only fit senior strikers.
Inter are currently fifth in the Serie A table and seven points shy of third-placed AC Milan ahead of Sunday's meeting with Atalanta at the San Siro, with games against Roma, Napoli and Lazio forming part of the eight-game run-in.